The possible cosmological variation of the proton-to-electron mass ratio was estimated by measuring the H_2 wavelengths in the high-resolution spectrum of the quasar Q~0347-382. Our analysis yielded an estimate for the possible deviation of mu value in the past, 10 Gyr ago: for the unweighted value $Delta mu / mu = (3.0pm2.4)times10^{-5}$; for the weighted value [ Delta mu / mu = (5.02pm1.82)times10^{-5}] Since the significance of the both results does not exceed 3$sigma$, further observations are needed to increase the statistical significance. In any case, this result may be considered as the most stringent estimate on an upper limit of a possible variation of mu (95% C.L.): [ |Delta mu / mu| < 8times 10^{-5} ] This value serves as an effective tool for selection of models determining a relation between possible cosmological deviations of the fine-structure constant alpha and the elementary particle masses (m$_p$, m$_e$, etc.).
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