The optimized expansion is applied to calculate the effective action for the Nambu-Jona-Lasinio model. The method is non-perturbative, the results derived from the effective action calculated to the first order of the optimized expansion corespond to an infinite summation of perturbative Feynman diagrams both in the Schwinger--Dyson equation for propagator and in the two-body Bethe--Salpeter equation. We show that this is equivalent to the mean field (relativistic Hartree plus random phase) approximation. The optimized expansion offers thus a systematic method to improve the relativistic mean field approximation in a consistent way.

PACS numbers: 03.70.+k, 21.60.Jz