A closure for the Ornstein-Zernike equation was proposed on the basis of an analysis of the properties of bridge functionals. The closure allows one to calculate the two-particle distribution function g(r) of the Lennard-Jones fluid with a relative error that does not exceed 1%-2% at all densities and temperatures. At the same time, the thermodynamic parameters of fluid in the same approximation are calculated with larger error. It has been shown that these facts are due to those additional errors that are entered by the formulas establishing the linkage between g(r) and thermodynamic parameters.