Frequency stability of a Rubidium Frequency Standard (RFS) is directly related to the signal-to-noise ratio (S/N) of the microwave-induced (6834 MHz) optical signal which is proportional to the fractional atomic population difference between the two M(F) = 0 ground state sublevels of Rb-87. In the present RFSs this fractional population difference is small (<1%). S/N can be substantially improved by concentrating all of the atoms in one of the two M(F) = 0 sublevels. Potentially, this could lead to a significant improvement in the short-term performance of RFSs. We have developed a novel scheme for concentrating a large fraction of the Rb atoms in one of the two M(F) = 0 ground state sublevels. We optically pump the Rb vapor with circularly polarized light from a AlGaAs diode laser tuned to the D-1 transition (794.7 nm), Nearly all of the atoms are concentrated in one of the two high angular momentum states (M(F) = 2 or -2 sublevels depending on the handedness of the circular polarization). The pumping laser is switched off and two radiofrequency (RF) pi-pulses are applied sequentially, The first pi-pulse transfers the atoms from the 2, 2 (F, M(F)) sublevel to the 2, 1 sublevel and the second pi-pulse transfers the atoms from the 2, 1 sublevel to the 2, 0 sublevel, The resulting population distribution is diagnosed using a second AlGaAs diode laser (weak probe) in conjunction with a microwave field tuned to the 0-0 transition (6834 MHz), We obtain a fractional population difference of 0.7-0.9 between the two M(F) = 0 sublevels. This should result in an improvement in the S/N by a factor of 70-90 over the lamp pumped RFSs. This could potentially be of considerable importance towards the development of future RFSs, Various relaxations and field inhomogenieties limit the transfer efficiency from being 100%. The details of the experimental technique and possible applications are discussed.