Valence ionization energies of a set closed-shell molecules calculated in a nondiagonal, renormalized approximation of the electron propagator have an average absolute error of 0.17 eV. This procedure extends the partial third order, quasiparticle approximation of J. Chem. Phys. 104, 7599 (1996) that has proven successful in many applications. Elements of the self-energy matrix include all second-order and many higher-order terms. Because of its fifth power dependence on basis set size and its independence from electron repulsion integrals with four virtual orbital indices, this method has considerable promise for large molecules. Formal and computational comparisons with renormalized electron propagator techniques that art complete through third-order illustrate die advantages of this procedure.