An investigation of the Orthogonalising Pseudo-Potential (OPP) introduced by Kukulin and Krasnopolsky is made with the emphasis on its numerical application. The OPP method is a projection operator technique to remove unwanted states from a many body calculation. An analysis of a model two level system was used to deduce the basic properties of the spectrum of the projected Hamiltonian. Detailed plots of the atomic properties of Na, Na-, Nae+ and NaPs were made as a function of the strength of the OPP to exhibit the operation of the OPP procedure for some complicated many-body systems. An improved wave function for the NaPs ground state was generated as a byproduct of this investigation. The current best estimates of the NaPs binding energy and annihilation rate are 0.008009 Hartree and 2.072x109 s-1, respectively.