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We develop a simple iterative algorithm for successive corrections of the correlation function and the free energy of a binary system. The main characteristics of the formalism are the use of an exact statistical-thermodynamic relations and the absence of the small parameters. The only approximation involved is the form of the configurational free energy which serves as a starting point for the iterative procedure. Two iterations within this algorithm for a dispersion-free and a microscopic model of fluctuations are presented starting with a one-site mean-field approximation. We obtain closed analytical expressions for the correlation function and thermodynamic potentials in each iteration. The algorithm can be widely applied, as in the calculation of phase diagrams, and segregation profiles at surfaces and thin films, and in k-space kinetic theories of atomic ordering and decomposition in alloys.