A pair-product projector, which projects onto an intrinsically Fermionic ground state, is implemented as part of a newly proposed Projection Monte Carlo method aimed at overcoming the Fermionic Sign Problem without employing the Fixed-Node approximation. Evaluating the fully anti-symmetrized pair- product projector requires factorial time. Three polynomial-time approximations are implemented and shown to be very close to the fully anti-symmetrized projector. A Fortran program is developed to generate configuration state functions for atomic systems using the projection method, with the goal of building all symmetries of a system into the trial wave functions used in Quantum Monte Carlo calculations. This brings an additional advantage of a significantly reduced number of variational parameters in trial wave functions. The program makes use of a bit-packed representation of Slater determinants and various algorithms to cut down run time and memory cost.