The two-configuration self-consistent field formalism previously presented in this Journal is extended and the CMC SCF LCAO MO (complete multi-configuration self-consistent field LCAO MO) technique is presented. The single Slater determinant for a 2n electron system is replaced by a combination of determinants built from two sets of MO's, one containing n orbitals; the second, (ω -n) orbitals. All the possible double excitations from the (n) set to the (ω -n) set are considered. The orbitals as well as the linear combination of determinants are simultaneously optimized making use of the self-consistent field technique. © 1967 Springer-Verlag.