Using the new limit on the neutrino anomalous magnetic moment recently obtained by GEMMA experiment we get an order-of-magnitude estimation for possible new direct upper bound on the neutrino electric millicharge $\mid q_{\nu} \mid \sim 1.5 \times 10^{-12} e_0e_0$ is the absolute value of the electron charge) by comparing the neutrino magnetic moment and millicharge contributions to the total cross section at the electron recoil energy threshold of the experiment. This estimation is confirmed by the performed analysis of the GEMMA data using established statistical procedures and a new direct bound on the neutrino millicharge absolute value $\mid q_{\nu} \mid < 2.7 \times 10^{-12} e_0 \ (90% CL)$ is derived. This limit is more stringent than the previous one obtained from the TEXONO reactor experiment data that is included to the Review of Particle Properties 2012.

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