The stopping power S = S₁ + S₂ for a charged particle in non-ideal plasmas (OCP) is calculated with the help of dielectric formalism accounting for the effects of second order (term S₂) in the field generated by the projectile. The theory allows to eliminate a number of discrepancies between experiments on slow (v_p < v_F) proton stopping in metals and the linear approximation S = S₁ (v_p is the projectile velocity, v_F is the Fermi velocity for the target plasma). The analysis of the term S₂, representing the Barkas effect for high projectile velocities v_p > v_F leads to an unexpected conclusion that in non-ideal plasmas the term S₂ ∼ v_p^-3, i.e. it decays with the velocity v_p much slower than according to the well-known law S₂ ∼ v_p^-5. This new regularity allows to explain a number of discrepancies between experimental values of S₂ for metals and the usual theory of the Barkas effect, without introducing fitted parameters.