An approach to symmetrize the liquid vapor phase coexistence curve is proposed. It is based on the introduction of the lattice-like density x = rho(1)/(rho(1)+ rho(2)), where rho(1) and rho(2) are the densities along the liquid-gas binodal. The global symmetrical phase diagram is created using experimental and simulation data for the real substances and models (noble gases, polyatomic molecules, organic substances and two metals, van der Waals system, Lennard-Jones system). The pressure and the temperature along the binodal are shown to satisfy some new similarity relations.