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Using the new limit on the neutrino anomalous magnetic moment recentlyobtained by the GEMMA experiment on measurements of the cross section for thereactor antineutrino scattering on free electrons, we get a new direct upperbound on the neutrino millicharge $\mid q_{\nu} \mid < 1.5 \times 10^{-12}e_0$. This is a factor of 2 more stringent constraint than the previous boundobtained from the TEXONO reactor experiment data that is included to the Reviewof Particle Properties 2012. We predict that with data from the ongoing newphase of the GEMMA experiment the upper bound on the neutrino millicharge willbe reduced to $\mid q_{\nu} \mid < 3.7 \times 10^{-13}e_0$ within two years. Wealso predict that with the next phase of the considered experiment the upperbound on the millicharge will be reduced by an order of magnitude over thepresent bound and reach the level $\mid q_{\nu} \mid < 1.8 \times 10^{-13}e_0$within approximately four years.

New bounds on neutrino electric millicharge from limits on neutrino magnetic moment