We study the properties of multiparticle direct correlations in detail and construct a system of successive approximations of the generating functional of direct correlation functions. Moreover, in contrast to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, this approach does not require approximating higher correlations. Our approximations determine the corresponding approximations of the thermodynamic potential. The irreducible parts of multiparticle direct correlations are constructed explicitly.