  We suggest to use a polarized electron target for improving the sensitivity
of the search for the neutrino magnetic moment to the level $\sim
3\cdot10^{-13}\mu_B$ in the processes of neutrino (antineutrino) -- electron
scattering. It is shown that in this case the weak interaction term in the
total cross section is significantly suppressed comparing with unpolarized
case, but the electromagnetic term does not depend on electron polarization.
