The main purpose of this work is to report on a calculation that describes the role of a long-range bridge function as applied to the study of the structure of simple liquid metals. We have drawn attention to the crossover integral equation method, which, in essence, amounts to adding to the long-range bridge function a short-range correction of bridge diagrams. The suggested crossover scheme has been tested for the case of liquid metal Cs at both the elevated and the supercooled liquid temperatures. Remarkably good results for the calculated liquid structures were obtained.