A molecular theory of biaxial nematic ordering in the system of bent-core molecules has been developed in the two-particle cluster approximation which enables one to take into account short-range polar correlations determined by both electrostatic dipole–dipole interaction and polar molecular shape. All orientational order parameters and short-range correlation functions are calculated numerically as functions of temperature in the uniaxial and in the biaxial nematic phases, and the results are compared with the ones obtained in the mean-field approximation and in the cluster approximation but without taking into consideration the dipole–dipole interaction. It is shown that short-range polar correlations and, in particular, the dipole–dipole correlations dramatically increase the temperature of the transition into the biaxial nematic phase and enhancing its stability range. The results are also very sensitive to the value of the opening angle of a model bent-core molecule.