  The double conversion of the neutrino helicity $\nu_L \to \nu_R \to \nu_L$
has been analyzed for supernova conditions, where the first stage is due to the
interaction of the neutrino magnetic moment with plasma electrons and protons
in the supernova core, and the second stage, due to the resonance spin flip of
the neutrino in the magnetic field of the supernova envelope. It is shown that,
in the presence of the neutrino magnetic moment in the range $10^{-13} \mu_{\rm
B} < \mu_\nu < 10^{-12} \mu_{\rm B}$ and a magnetic field of $\sim 10^{13}$ G
between the neutrinosphere and the shock-stagnation region, an additional
energy of about $10^{51}$ erg, which is sufficient for a supernova explosion,
can be injected into this region during a typical shock-stagnation time.
