The stopping power S=S1+SB for charged particles in non-ideal degenerate quantum plasmas is calculated with the help of the dielectric formalism in an approximation corresponding to taking account of the Barkas effect (the term SB; the term S1 corresponds to the Bethe formula). It is found that for a high projectile velocity vp>vF (where vF is the Fermi velocity) in non-ideal plasmas, SB∝e3pv−3p (where ep is the charge of the projectile), the well-known law for the Barkas effect, SB∝e3pv−5p being valid only for ideal plasmas. This relation explains a number of experiments on stopping of different charged particles (protons, muons and heavy ions) in metals without the introduction of fitted parameters. The possibility of extending of this theory to gaseous non-ideal plasmas arising in inertial-confinement fusion (ICF) experiments is also briefly discussed.