We present an alternative formulation of perfect pairing (PP) aimed at giving a more faithful representation of the valence correlation energy of an arbitrary molecule. In the new theory, the occupied and virtual orbitals are nonorthogonal amongst themselves but orthogonal to each other. Whereas for the fully orthogonal version of PP one has the number of pairs equal to the number of occupied orbitals, the current formulation allows for an arbitrary number of pairs built from redundant orbitals. We propose setting the number of pairs equal to the number of valence orbitals in the molecule. Preliminary results indicate that the redundant formulation gives qualitatively improved results for delocalized systems such as benzene, while maintaining the attractive features of PP for localized systems. (C) 2000 American Institute of Physics. [S0021-9606(00)30511-6].