The effect of reintroducing the overlap matrix into the secular equations for an NDDO (neglect of diatomic differential overlap)-based semiempirical molecular orbital method has been investigated. The modification is expected to improve the description of interactions between electron pairs. The idea has been tested by implementation and evaluation of a nonorthogonal version of the MNDO method (NO-MNDO) with parametrization for hydrogen, carbon, nitrogen, and oxygen. Overall, the accuracy of NO-MNDO for heats of formation is nearly identical to that for the more highly parametrized AM1 method. The mean absolute error (MAE) for heats of formation of a comprehensive set of 622 neutral, closed-shell molecules is reduced from 8.4 kcal/mol with MNDO to 6.8 kcal/mol with NO-MNDO. In addition, the performance for conformational equilibria and torsional barriers is significantly improved with NO-MNDO, presumably owing to the improved description of closed-shell interactions. For molecular geometries, the usual training and test sets have been expanded through use of MP2/6-31G(d) results for consistent comparisons. The performance of NO-MNDO for bond lengths, bond angles, and dihedral angles remains good with MAEs of 0.017 Å, 2.5°, and 4.5°. Additionally, NO-MNDO corrects severe errors by MNDO for R(•) + H-R' hydrogen-atom transfers, while testing for activation barriers for nine pericyclic reactions reveals only modest improvement.