We introduce a new self-consistent summation procedure for the analysis of Feynman-Dyson perturbation series and demonstrate how a self-consistent expression for the self-energies of an interacting system may be obtained. We obtain the simplest self-consistent solution to the problem of an interacting many fermion system exhibiting long-range order, characterised by the existence of anomalous propagators, in which correlation effects not described by the Hartree-Fock-Gorkov approximation are important.