As an extension of the method presented in reference [4], this paper concerns with the transformation from Ising spin S=1 systems to a Fermion system in which the total number of particles is not a constant. We obtained rigorously the ground state energy of the antiferromagnetics of Ising S=1 fcc lattice with nearest neighbors and next nearest neighbors interaction in an arbitrary magnetic field, and also the phase equilibrium diagram at T = OK.