In this paper, we address the modular verification problem for a Petri net obtained by composition of two subnets. At first, we show how to transform an asynchronous composition into a synchronous one where the new subnets are augmented from the original ones by means of linear invariants. Then we introduce a non-constraining relation between subnets based on their behaviour. Whenever this relation is satisfied, standard properties like the liveness and the boundedness and generic properties specified by a linear time logic may be checked by examination of the augmented subnets in isolation. Finally, we give a sufficient condition for this relation which can be detected modularly using an efficient algorithm.