This paper presents a new self-consistent dressing of a singles and doubles configuration interaction matrix which insures size-consistency, separability into closed-shell subsystems if localized molecular orbitals (MOs) are used, and which includes all fourth order corrections. This method yields, among several schemes, a reformulation of the coupled cluster method, including fully the cluster operators of single and double excitations, and partially those of the triples (Bartlett’s algorithm named CCSDT-1a). Further improvement can be easily included by adding exclusion principle violating corrections. Since it leads to a matrix diagonalization, the method behaves correctly in case of near degeneracies between the reference determinant and some doubles. Due to its flexibility this formulation offers the possibility of consistent combination with less expensive treatments for the study of very large systems.