A method for regular improvement of the mean field approximations for lattice systems is proposed. The method requires transcription of the initial lattice to a new lattice of complex sites each representing the states of several initial sites. This approach is valuable for the description of many-particle distributions on the lattice. The validity of this approach is tested by comparison of the coexistence curve, the concentration dependence of the probabilities for two lattice sites to be vacant and the jump diffusion coefficients for two-dimensional square lattice gas with Monte Carlo simulation data.