We introduce the electron-nuclei general mean field configuration interaction (EN-GMFCI) approach. It consists in building an effective Hamiltonian for the electrons taking into account a general mean field due to the nuclear motion and, conversely, in building an effective Hamiltonian for the nuclear motion taking into account a general mean field due to the electrons. The eigenvalue problem of these Hamiltonians are solved in a basis set giving partial eigensolutions for the active degrees of freedom (dof), that is to say, either for the electrons or for the nuclear motion. The process can be iterated. If first-order effective Hamiltonians, averaged over the ground state (GS) of the non-active or ''spectator'' dof, are chosen at every step of the process, the total energy corresponding to the product of the electronic GS wave functions by the nuclear motion GS wave function, can only decrease. The EN-GMFCI is a new paradigm for quantum chemistry that bypasses the traditional Born-Oppenheimer (BO) reduction of the molecular \sch equation to an electronic problem and a nuclear poblem. In the EN-GMFCI method, electron and nuclei are treated on the same footing. In contrast with the BO or adiabatic decoupling schemes, the electronic potential for the nuclei is known exactly and analytically from a single electronic calculation. So there is no need to perform electronic calculations for a large grid of nuclear configurations and to fit a PES. The method is illustrated on diatomic molecules.