In this paper, we analyze the effect of the invariance weakness defined by Fluhrer, Mantin and Shamir in [8] on the a new variant of RC4 Key-Scheduling Algorithm, called KSAm, proposed by Crainicu and Boian in [2]. We demonstrate that the state permutation S of the RC4 with KSAm after running the new Scrambling_1 component introduced by KSAm is not b-conserving, which means that KSAm does not expose the invariance weakness, being therefore capable to strengthen the overall RC4 stream cipher. We also propose an algorithmic approach model for the identification of the mappings of the secret key bits to identifiable patterns in the initial permutation S. The propsed model is suitable for testing any Scrambling-like mechanism applied to a permutation, where the values of two entries are swapped at each step.