The magnetic field in the solar convective zone has a random small-scale co
mponent with a r.m.s. value substantially exceeding the strength of a regul
ar large-scale field. In the presence of a neutrino transition magnetic mom
ent we find an effective production of electron antineutrinos in the Sun ev
en for small neutrino mixing through the cascade conversions in the random
magnetic field that would be a signature of the Majorana nature of neutrino
if AR were registered. Basing on the present SK bound on electron antineut
rinos we also estimated the corresponding excluded area in the plane Delta
m(2), sin(2)2 theta.