The notion of pseudo-free groups was first introduced and formalized by Hohenberger and Rivest in order to unify cryptographic assumptions. Catalano, Fiore and Warinschi proposed a generalized notion called adaptive pseudo-free groups, and showed that the RSA group $\Z_N^\times$ is adaptive pseudo-free with some specific parametric distribution under the strong RSA assumption. In this paper, we develop an alternative parametric distribution and show that the RSA group $\Z_N^\times$ is adaptive pseudo-free with the parametric distribution under the RSA assumption rather than the strong RSA assumption.