  The process of the two-step conversion of the neutrino helicity, $\nu_L \to
\nu_R \to \nu_L$, is analysed in the supernova conditions, where the first
stage is realized due to the interaction of the neutrino magnetic moment with
the plasma electrons and protons in the supernova core. The second stage is
caused by the neutrino resonant spin-flip in a magnetic field of the supernova
envelope. Given the neutrino magnetic moment within the interval $10^{-13}
\mu_{\rm B} < \mu_\nu < 10^{-12} \mu_{\rm B}$, and with the existence of the
magnetic field at the scale $\sim 10^{13}$ G between the neutrinosphere and the
shock-wave stagnation region, it is shown that an additional energy of the
order of $10^{51}$ erg can be injected into this region during the typical time
of the shock-wave stagnation. This energy could be sufficient for stumulation
of the damped shock wave.
