Judgments, Supreme Court, New York County (Rena K. Uviller, J.), rendered January 11, 2006, convicting defendant, upon his plea of guilty, of criminal sexual act in the third degree, falsifying business records in the first degree (four counts), forcible touching (three counts), attempted forcible touching (three counts) and bail jumping in the second degree, and sentencing him to an aggregate term of 4 to 12 years, unanimously modified, on the law, to the extent of vacating the supplemental sex offender fee, and further modified, as a matter of discretion in the interest of justice, to the extent of vacating the provisions of the orders of protection that directed that they remain in effect[*400] until January 10, 2021, and otherwise affirmed, and the matter remanded for a new determination of the duration of those orders.

The court properly imposed consecutive sentences for the separate and distinct crimes of criminal sexual act in the third degree and falsifying business records in the first degree. An element of the latter crime is that a defendant’s “intent to defraud includes an intent to commit another crime or to aid or conceal the commission thereof’ (Penal Law § 175.10). However, criminal sexual act is not, by definition, an essential element of first-degree falsifying business records. Furthermore, a conviction of that crime does not require the actual commission of the crime the defendant intended to conceal (People v McCumiskey, 12 AD3d 1145 [2004]). Therefore, even if, according to his plea allocution, defendant falsified the records at issue for the purpose of concealing the sex crime to which he also pleaded guilty, consecutive sentences were permissible (see Penal Law § 70.25 [2]; People v Laureano, 87 NY2d 640, 643 [1996]).

We perceive no basis for reducing the sentence.

As the People concede, the expiration date on the orders of protection is erroneous since it was calculated without taking into account the jail time credit to which defendant is entitled. Although defendant failed to raise this issue before the sentencing court, we reach this issue in the interest of justice.

As the People also concede, since the crime was committed prior to the effective date of the legislation (Penal Law § 60.35 [1] [b]), providing for the imposition of a supplemental sex offender fee, that fee should not have been imposed. Concur— Lippman, P.J., Marlow, Williams and Gonzalez, JJ.