Within the framework of the second order perturbation theory by the pseudopotential of the electron-ion interaction, the equation of state of liquid metallic helium is obtained. The pseudopotential found earlier from the first principles by one of the authors, was used. This pseudopotential, according to the general theory of pseudopotentials is nonlocal and nonlinear. The nonlocality of the pseudopotential leads to the fact that in the decomposition of the internal energy of the liquid metallic helium a member of the first order is present in a series of pseudopotentials. Its diagonal matrix element is of the same order of magnitude as the zero-order member. In the calculation of the pressure of liquid metallic helium, this pressure is significantly higher than when using simple local potentials and an order of magnitude higher than for liquid metallic hydrogen. This fact explains the fact that hydrogen in the metallic state has long been obtained, while the existence of metallic helium has not yet been experimentally proven.