A new approximate bridge function is proposed as an expansion in powers of the thermal potential, which ensures the thermodynamic consistency with the classical pressure-compressibility condition. The bridge function compares very well the simulation data at large separation as well as in the most important region of the core. The thermodynamic properties of the supercritical Lennard-Jones fluid calculated by means of standard formulas of statistical mechanics involving correlation functions and bridge function are in excellent agreement with those obtained from computer simulation. (C) 2003 American Institute of Physics.