The recently implemented second-order perturbation theory based on a complete active space self-consistent field reference function has been extended by allowing the Fock-type one-electron operator, which defines the zeroth-order Hamiltonian to have nonzero elements also in nondiagonal matrix blocks. The computer implementation is now less straightforward and more computer time will be needed in obtaining the second-order energy. The method is illustrated in a series of calculations on N2, NO, O2, CH3, CH2, and F−.