A new method for improving the limit on the electric charge of the neutrino is suggested. The method relies on generating an alternative potential between a metallic hemisphere and ground by a time-oscillating neutrino beam. The transitions between hyperfine sublevels of polarized nuclei undergoing beta decay are used to produce the time-oscillating neutrino beam. The estimates suggest that the upper limit achievable on neutrino electric charge may reach 10^-12e₀, where e₀ is an electron charge.