We have developed previously ab initio molecular dynamics (AIMD) algorithms utilizing local molecular wave functions with atom-centered bases. The expense of such methods led us to explore means to employ multiple time step schemes to reduce costs. Herein we report our second implementation of such a scheme. Tn particular, our previous multiple time step AIMD method has been improved substantially by the implementation of the time-reversible reference system propagator algorithm (RESPA) of Berne and co-workers. The time-reversible version of RESPA treats multiple time steps rigorously without introducing the limitations inherent in our previous non-time-reversible AIMD RESPA implementation. We are thus simultaneously able to obtain substantial additional savings in computer time and to maintain high accuracy, as shown in test calculations on a sodium cluster.