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We report a new precise determination of the leptonic widths of the J/psi meson performed with the KEDR detector at the VEPP-4M e+e-collider.The measured values of the J/psi parameters are: Гee×Гee/Г =0.3323±0.0064(stat.)±0.0048(syst.)keV,Гee×Гμμ/Г = 0.3318±0.0052(stat.)Г0.0063(syst.)keV.Assuming eμ universality and using the table value of the branching ratios the leptonic Г11 = 5.59±0.12 keV width and the total Г = 94.1±2.7 keV widths were obtained.We also discuss in detail a method to calculate radiative corrections at a narrow resonance.