Abstract The Perturbational Molecular Orbital (PMO) theory for non-degenerate Hamiltonian is presented in matrix notation. As a consequence of this formulation, a practical algorithm to obtain analytical and numerical expressions up to any order is described. Degenerate perturbation theory is also discussed in the context of the present formulation of PMO theory. A simpler two state problem is examined to illustrate the convergence of the PMO expansion. Finaly, an heuristic convergence criterion is presented.