Including in the definitions of correlation functions singular corrections that describe "self-correlatio ns," it is possible to find a rigorous, almost trivial solution of the complete BBGKY hierarchy for a system of charged particles corresponding to motion of them in a self-consistent field. Study of the averaged small deviations from this motion makes it possible to construct a scheme of successive approximations. In this manner, an expansion is obtained for the single-particle distribution function which is equivalent to a generalization of Grad's moment method to the phase space. In the first order of perturbation theory, an approximate Lenard-Balescu equation that differs from the result of its direct linearization is obtained. The proposed approach makes possible a more consistent approximate treatment of statistical systems.