An approximate expression for the electron-electron repulsion energy of a closed-shell four-electron system in terms of the Coulomb and exchange integrals among natural orbitals and the respective occupation numbers is derived. It constitutes a strict upper bound to the exact density matrix functional, yields energy that is lower than that obtained within the antisymmetrized product of strongly orthogonal geminals theory, and thus is exact for two noninteracting two-electron systems. Its relevance to the general case of closed-shell N-electron systems is discussed. (C) 2003 American Institute of Physics.