Abstract The Falicov‐Ramirez‐Kimball model is solved by means of the two‐atom cluster Caron‐Pratt approximation. Metallic and insulating phases according to the value of an order parameter Δ are obtained, and both second‐ and first‐order phase transitions between them. Two kinds of insulating solutions (ordinary and mixed valence) and a variety of metallic states with different inter‐ionic degrees of correlation are obtained. These results are found to be inqualitative accord both with experiments and former theoretical treatments.