  The magnetic field in the convective zone of the Sun has a random small-scale
component with the r.m.s. value substantially exceeding the strength of a
regular large-scale field. For two Majorana neutrino flavors $\times$ two
helicities in the presence of a neutrino transition magnetic moment and nonzero
neutrino mixing we analyze the displacement of the allowed ($\Delta m^2-
\sin^22\theta$)-parameter region reconciled for the SuperKamiokande(SK) and
radiochemical (GALLEX, SAGE, Homestake) experiments in dependence on the r.m.s.
magnetic field value $b$, or more precisely, on a value $\mu b$ assuming the
transition magnetic moment $\mu = 10^{-11}\mu_B$. In contrast to RSFP in
regular magnetic fields we find an effective production of electron
antineutrinos in the Sun even for small neutrino mixing through cascade
conversions $\nu_{eL}\to \nu_{\mu L}\to \tilde{\nu}_{eR}$, $\nu_{eL}\to
\nu_{\mu R}\to \tilde{\nu}_{eR}$ in a random magnetic field that would be a
signature of the Majorana nature of neutrino if $\tilde{\nu}_{eR}$ will be
registered. Basing on the present SK bound on electron antineutrinos we have
also found an excluded area in the same $\Delta m^2,~\sin^22\theta$-plane and
revealed a strong sensitivity to the random magnetic field correlation length
$L_0$.
