Appellants Melvin S. Dick and Anthony Giacomino appeal their convictions on twenty counts of mail fraud and providing false statements to a federal agency. We , reverse on several counts, but affirm on the remaining counts.

I.

Appellants were convicted in a bench trial for scheming to defraud two bonding companies, the United States, and the United States Small Business Administration (SBA) of money paid by the sureties on a defaulted construction contract performance bond, ninety percent of which was reimbursed by the SBA. Appellant Giacomino owned a construction company which the sureties hired to complete the work after the principal’s default. Appellant Dick was outside counsel to the sureties who let the contract to Giacomino on their behalf.

Viewing the evidence in the light most favorable to the government, Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942), the facts may be distilled down to the following. Bergen Construction Corporation was the general contractor on construction of the Far North Police Station for the City of Chicago. Bergen solicited bids from subcontractors to perform the concrete work on the project, and awarded the concrete subcontract to Minority Builders, Inc., for $213,-500. Minority secured the required performance bond from two sureties, Heritage Insurance Company of America, the lead carrier, and American Fidelity Fire Insurance Company, the secondary carrier. Both sureties participated in the SBA’s surety bond guarantee program, 15 U.S.C. §§ 694a-694c (1982). The program, enacted by Congress in 1970 to enable small contractors to obtain performance bonds, provides reimbursement for ninety percent of the losses incurred by participating sureties on performance bonds issued to qualified small contractors such as Minority.

Minority commenced work on the project in October 1976, and, after experiencing various difficulties, abandoned the project in early September 1977. At that time Minority estimated that the project was ninety percent complete and would cost[*549] some $40,000-$50,000 to finish; eighty-eight percent of Minority’s progress payments had been approved, less a standard ten percent retained for repairs.

Appellant Dick, an attorney employed by Heritage since 1974 to handle its performance bonds, represented the sureties on the Minority performance bond. Dick thus was responsible for retaining a “completion contractor” to complete the work not finished by Minority and for minimizing the loss to the sureties. Bergen, the general contractor, informed Dick that with some qualifications it would finish Minority’s contract work, but Dick replied that he would arrange for a completion contractor to finish the work. Dick hired appellant Giacomino’s State Construction Company as the completion contractor at a cost of $196,000. Giacomino in turn subcontracted with Concrete Structures of the Midwest to perform most or all of State’s contractual obligations on the project at a contract price of $88,650, which had been bargained up by Giacomino from Concrete Structures’ initial estimate of $87,500. In the various transactions surrounding performance of the completion contract, the fact that Concrete Structures rather than State actually was performing the work was concealed from Bergen, the sureties, and the SBA.

Dick informed Heritage and the SBA that he had solicited bids for the completion work, although he was not required to do so. He mailed to Heritage and the SBA a letter reporting four telephone bids, for which there was no documentation in his files. State appeared as the low bidder. This letter did not mention any written bids, but Dick had in his files four written bids, including one from State, that pre-dated the reported telephone bids. The written bids were in the same amounts as the telephone bids, but the bids other than State’s were on behalf of different companies. State again appeared as the low bidder. The district court found that all the bids except State’s were false, and that Giacomino had participated in the preparation of one of the rigged bids. ^[1]

Appellants were indicted for scheming to defraud Heritage and American Fidelity of money, the loyal services of their attorney, and the right to have completion contracts fairly awarded; for scheming to defraud the United States and the SBA of money and their right to have the bond guarantee program honestly conducted; and for making false material statements in a matter within the jurisdiction of a federal agency. Of the twenty-count indictment, counts 1-11 ^[2] were under the mail fraud statute, 18 U.S.C. § 1341 (1982), and counts 12-20 ^[3] were under the false statements statute, 18 U.S.C. § 1001 (1982). Both appellants were convicted on all twenty counts. ^[4]

[*550] Appellants argue on appeal that, with regard to the mail fraud counts: (1) there was insufficient evidence to prove the participation of either appellant in a scheme to defraud; (2) no scheme to defraud could exist without proof of a bribe or kickback; and (3) certain of the mailings were not for the purpose of executing the scheme to defraud. On the false statements counts, appellants argue that: (1) there was insufficient evidence that the false statements were material; and (2) there was insufficient evidence that appellants knowingly-made false statements and deliberately conveyed them to the SBA.

II.

Under the mail fraud statute, the government must prove a scheme to defraud and a mailing made for the purpose of executing such a scheme. Pereira v. United States, 347 U.S. 1, 8, 74 S.Ct. 358, 362, 98 L.Ed. 435 (1954). Appellant Giacomino challenges the finding that he participated in a scheme to defraud, essentially arguing that he did nothing wrong. Giacomino asserts a lack of evidence showing that the completion contract between State and Heritage was inflated. Without such evidence, he claims, we must assume the contracting parties dealt at arm’s length; he maintains that the fact that the contract happened to benefit him hardly proves his participation in a scheme to defraud. ^[5]

We may reject Giacomino’s argument out of hand. Proof of pecuniary loss is not essential to a mail fraud conviction. United States v. Lea, 618 F.2d 426, 429 n. 3 (7th Cir.), cert. denied, 449 U.S. 823, 101 S.Ct. 82, 66 L.Ed.2d 25 (1980). This court has recognized that breach of a fiduciary duty to disclose information to an employer can support a mail fraud conviction where such information was material to the conduct of the employer's business and nondisclosure could or does result in harm to the employer. United States v. Feldman, 711 F.2d 758, 763 (7th Cir.), cert. denied, — U.S. -, 104 S.Ct. 352, 78 L.Ed.2d 317 (1983); accord United States v. Bronston, 658 F.2d 920, 926 (2d Cir.1981), cert. denied, 456 U.S. 915, 102 S.Ct. 1769, 72 L.Ed.2d 174 (1982). As counsel to the sureties in charge of the Minority performance bond, Dick owed them a fiduciary duty of honest, loyal, and faithful performance, which certainly would include proper management of the loss, full and accurate reporting of his activities, and above all protecting the sureties’ interests. Instead, Dick concealed the method by which he selected State as the completion contractor and set the completion contract price, and concealed the fact that the bulk of the work was subcontracted out to Concrete Structures for a substantially lower amount. ^[6] Although Giacomino casts him[*551] self as the lucky beneficiary of a favorable bargain who did not lie to win the contract and owed no fiduciary duty to the sureties, his role as a coschemer in the breach of Dick’s fiduciary duty was proven by his personal efforts to conceal the realities of his contract award.

Appellant Dick asserts that the evidence was insufficient to prove his knowing and intentional participation in the scheme to defraud. In his strongest argument on this point, Dick attempts to show that he unintentionally made certain false statements to the consultant he hired, Heritage, and the SBA concerning Minority’s original bid on the concrete work. These allegedly innocent mistakes happened to provide support for a completion contract at nearly the full amount of the original concrete contract, and happened to augment Dick’s assertion that Minority had substantially underbid the project. Dick’s selective recall of the amount of Minority’s original bid can be explained only by finding deliberate or at least reckless mishandling of information he was under a fiduciary duty to disclose accurately. Reckless disregard for truth or falsity is sufficient to sustain a conviction for mail fraud. See United States v. Farris, 614 F.2d 634, 638 (9th Cir.1979), cert. denied, 447 U.S. 926, 100 S.Ct. 3022, 65 L.Ed.2d 1120 (1980); United States v. Frick, 588 F.2d 531, 536 (5th Cir.), cert. denied, 441 U.S. 913, 99 S.Ct. 2013, 60 L.Ed.2d 385 (1979). Dick’s claim of confusion or ignorance cannot be countenanced to excuse him from knowing participation in the scheme. Mistakes such as these, together with the discrepancies in the written and reported telephone bids and other of Dick’s statements and activities, prove his knowing and intentional participation in the scheme to defraud.

Appellant Giacomino also argues that receipt of a bribe or kickback is an essential element in a scheme to defraud. Here, the evidence showed that a company owned by Giacomino had provided Dick with free landscaping materials and services; the value of the landscaping was disputed. While most cases have involved some financial gain to the one breaching his fiduciary duty, they have not required financial gain. See, e.g., United States v. Bryza, 522 F.2d 414, 421-22 (7th Cir.1975), cert. denied, 426 U.S. 912, 96 S.Ct. 2237, 48 L.Ed.2d 837 (1976); United States v. George, 477 F.2d 508, 513 (7th Cir.), cert. denied, 414 U.S. 827, 94 S.Ct. 49, 38 L.Ed.2d 61 (1973). We affirm the district court and hold that a bribe or kickback is not a prerequisite to a scheme to defraud under the mail fraud statute. ^[7] Appellants appeal their convictions on counts 1, 2, and 8 only on the grounds that no scheme to defraud existed; we thus affirm appellants’ convictions on these counts.

Appellant Dick argues that the mailings which form the bases of counts 3, 4, 5, 7, 9, 10, and 11 were not for the purpose of executing the scheme to defraud as required by statute ^[8] and case law, see, e.g., United States v. Wormick, 709 F.2d 454, 462 (7th Cir.1983) (mailing must be not only caused by schemers, but for the purpose of executing the scheme); United States v. Lea, 618 F.2d 426, 430 (7th Cir.), cert. denied, 449 U.S. 823, 101 S.Ct. 82, 66 L.Ed.2d 25 (1980).

Counts 3, 4, and 7 were based on mailings to Bergen of letters about the scheduling of concrete work at the site. Two letters were from Giacomino (counts 3 and[*552] 4) and one was from the consultant hired by Dick, listing the items remaining to be performed under the completion contract (count 7). ^[9] Dick first asserts that he did not cause the mailings from Giacomino and thus cannot be charged with these counts. However, conspiracy doctrines apply in a multi-party mail fraud scheme such as this even absent a separate conspiracy count. See United States v. Wormick, 709 F.2d 454, 461 (7th Cir.1983); United States v. Wilson, 506 F.2d 1252, 1257 (7th Cir.1974). If these mailings were for the purpose of executing a scheme to defraud of which he was a party, Dick “can be held accountable for mailings caused by other members [of the scheme], whether or not he knew of or agreed to any specific mailing.” Wormick, 709 F.2d at 461.

The government contends that these mailings were a means of concealing from Heritage and the SBA the role of Concrete Structures as a subcontractor and conveying the appearance that State actually was performing the work. The government further argues that the three mailings to Bergen, the general contractor, were instrumental to the most important part of the scheme: completing the work so Giacomino could be paid. We do not feel constrained to adopt the government’s position on these counts. We cannot say that because State won the completion contract under a scheme to defraud, all of State’s efforts to get the work done were for the purpose of executing the scheme. The scheme to defraud consisted of appellants’ efforts to conceal from the sureties and the SBA, not Bergen, the method by which Dick selected State as the completion contractor and information which would reflect on the contract price. Bergen presumably had no interest in who actually performed the work or at what price, as long as the work was done. Thus the mailings to Bergen were not for the purpose of executing the scheme to defraud. We reverse both appellants’ convictions on counts 3, 4, and 7.

Count 5 was based on a copy of the count 4 letter to Bergen that Giacomino mailed to Dick. The mailing to Dick, who as representative of the sureties was likely to retransmit its contents in some manner to the sureties or simply to put the letter in the Minority file, was for the purpose of executing the scheme. We affirm appellants’ convictions on count 5.

Counts 9, 10, and 11 were based on mailings of reimbursement checks from the SBA to Heritage, which Dick argues occurred after the scheme had ended. ^[10] Dick claims that the scheme was complete when State received payment from Heritage rather than when the SBA reimbursed Heritage. The reimbursements, however, were part of the fruit of the scheme. Dick knew that the SBA would cover ninety percent of the sureties’ loss on the Minority bond. Also aware of that fact, Heritage may have given Dick more leeway than it would have otherwise in letting the completion contract. Further, the regulations promulgated under the statutory mandate for the guarantee program require sureties, in order to qualify for the SBA guarantee, to affirm that without the guarantee they would not issue the bond to the principal. 13 C.F.R. § 115.6(a)(3) (1983). We hold that the scheme did not reach fruition until the SBA had reimbursed the sureties, and the mailings of the reimbursement checks were chargeable as part of the mail fraud scheme. Cf. United States v. Maze, 414 U.S. 395, 402, 94 S.Ct. 645, 649, 38 L.Ed.2d 603 (1974). Appellants’ convictions on these counts are affirmed.

III.

A section 1001 conviction requires proof of a false material statement made knowingly and willfully in a matter within the jurisdiction of a federal agency. Unit [*553] ed States v. Petullo, 709 F.2d 1178, 1180 (7th Cir.1983). Appellants first urge reversal of the false statements counts due to insufficient evidence that the false statements were material or affected in any way the government agency’s action. Appellants note that under the SBA program, the sureties were not obligated to provide the SBA with the bid description, consultant’s reports, lien waivers, and contractor’s affidavits which eventually came into SBA hands in this case and form the bases for the false statements counts. ^[11]

Under section 1001 a false statement may be material even though the agency did not rely on it and was not influenced by it. We have held that a false or fraudulent statement must have had only the natural tendency to influence, or have been capable of influencing, the agency. See United States v. Di Fonzo, 603 F.2d 1260, 1266 (7th Cir.1979), cert. denied, 444 U.S. 1018, 100 S.Ct. 672, 62 L.Ed.2d 648 (1980). Accord United States v. Richmond, 700 F.2d 1183, 1188 (8th Cir.1983); United States v. Diaz, 690 F.2d 1352, 1357-58 (11th Cir.1982). That a statement was not required to be made to the agency does not make the statement any less material. Diaz, 690 F.2d at 1358.

Each of the statements charged in counts 12-20 misrepresented the circumstances establishing the amount the sureties would pay out on the loss and consequently the amount in which the SBA would reimburse the sureties. The statements, either explicitly false or misleading due to omissions, had the natural tendency to influence the SBA in its handling of this guarantee either during the reimbursement stage or later during a possible audit. These false statements were material within the meaning of the false statements statute.

Appellants next contend that their knowledge of the falsity of the statements underlying counts 12-20 was not proven. The government bore the burden of proof that each appellant acted with the knowledge that each statement charged was false or with the conscious purpose of avoiding the truth. United States v. West, 666 F.2d 16, 19 (2d Cir.1981). Proof of knowledge that federal funds were involved is not required. United States v. Stanford, 589 F.2d 285, 297 (7th Cir.1978), cert. denied, 440 U.S. 983, 99 S.Ct. 1794, 60 L.Ed.2d 244 (1979); United States v. Baker, 626 F.2d 512, 515-16 (5th Cir.1980).

The statements underlying counts 12 and 13 reflected deliberate and knowing falsifications made by Dick. The count 12 letter described purported telephone bids which the district court found Dick had falsified; we see no reason to reverse. The count 13 letter was a consultant’s report offering as the reason for Heritage’s loss on the performance bond Minority’s substantial underbid on the project. In making the report, the consultant predictably relied on information given him by Dick as to Minority’s original bid. We also see no reason to reverse the district court’s finding that Dick deliberately misrepresented the amount of Minority’s bid to make the completion contract amount appear more reasonable. We hold that Dick knowingly and willfully gave the consultant false information with the expectation that it would be used in the preparation of misleading reports to the sureties and the SBA. We affirm Dick’s convictions on these two counts.

The government offered no proof linking appellant Giacomino to the statements of counts 12 and 13. While Giacomino would have known that these statements were false and presumably would have desired their making as necessary to facilitate the overall scheme to defraud, the government did not attempt to show that Giacomino either participated in[*554] their making or was even aware that they were made. The evidence clearly cannot support Giacomino’s conviction as a principal on these false statements counts. The false statements statute has not been held to incorporate conspiracy principles, as has the mail fraud statute, see United States v. Wormick, 709 F.2d 454, 461 (7th Cir.1983), and the government did not argue at trial or on appeal that Giacomino was an aider and abettor rather than a principal on these counts. Had the government presented an aiding and abetting theory, the district court could have convicted Giacomino as such despite the indictment’s failure to include an aiding and abetting count. See United States v. Galiffa, 734 F.2d 306 (7th Cir.1984) (jury instruction on aiding and abetting held not fatal variance from indictment, although no such count in indictment); United States v. Tucker, 552 F.2d 202, 204 (7th Cir.1977) (no unfairness in bench trial conviction for aiding and abetting although no such count in indictment). We therefore reverse Giacomino’s convictions on counts 12 and 13.

Counts 14-20 involved altered lien waivers and false contractor’s affidavits which were in Dick’s Minority file. Appellants argue that the false statements contained therein were not deliberately made to the agency because they were placed in Dick’s files, which appellants did not expect the SBA to examine. Neither the statute nor case law, however, requires that the false statements be conveyed to the government agency, let alone that appellants deliberately convey them. This issue usually arises in the context of a claim that the false statements did not concern a matter within the jurisdiction of a federal agency, as where the government’s involvement is limited to reimbursements. We have held that the false statements need not be submitted directly to a government agency, provided that, as here, the agency retains ultimate authority to see that federal funds are disbursed properly. See United States v. Petullo, 709 F.2d 1178, 1180 (7th Cir. 1983); United States v. Stanford, 589 F.2d 285, 297 (7th Cir.1978), cert. denied, 440 U.S. 983, 99 S.Ct. 1794, 60 L.Ed.2d 244 (1979). Even if the false statements never reached the SBA, the making of the statements to the sureties would suffice to violate section 1001 because the SBA in turn would rely on the sureties’ statements to it.

The district court found Giacomino responsible for alteration of the lien waivers ^[12] as they passed from the materials supplier to the purchaser, Concrete Structures, then to Giacomino at State and on to Dick’s Minority file. The district court noted that despite their lack of legal significance, the alterations suggested that State rather than Concrete Structures was performing the work on the job, and that the job was much larger than it actually was. While we have no doubt that the alterations were performed by or at the direction of either Giacomino or Dick, the government offered no proof as to which appellant did the deed. The trial judge’s opinion provides no insight as to why he found that Giacomino rather than Dick made the alterations, other than his immediately preceding finding that Giacomino was responsible for preparation of one of the phony written bids. We hold that the government has failed to meet its burden of proving beyond a reasonable doubt that either appellant altered or aided and abetted the alteration of the lien waivers and thus may be convicted for making the false statements therein. ^[13] We reverse both appellants’ convictions on counts 14-16.

The contractor's affidavits exhibited Giacomino’s sworn statements that “[t]he names of all parties who have furnished or who have been contracted with by affiant to furnish material or labor” were included in the affidavit. Giacomino[*555] made knowing falsifications by failing to mention Concrete Structures as a contracting party. Dick likewise made knowing falsifications by placing the affidavits in the Minority file. We affirm the convictions of both appellants on counts 17-20.

IV.

In sum, we reverse the convictions of appellant Dick on counts 3, 4, 7, 14, 15, and 16. ^[14] We reverse the convictions of appellant Giacomino on counts 3, 4, 7, 12, 13, 14, 15, and 16. ^[15] Because the district court sentenced appellants separately on each count, their prison and probation terms remain intact despite reversal of these counts. Cf. United States v. Wormick, 709 F.2d 454, 463 (7th Cir.1983) (sentence of two-year prison term on one count followed by five years probation on four counts remanded for discretionary re-sentencing upon reversal of one of the probation counts).