We present measurements of the branching fractions for J/psi -> e(+)e(-) and mu(+)mu(-) using 3M psi(2S) decays collected with the CLEO detector operating at the CESR e(+)e(-) collider. We obtain B(J/psi -> e(+)e(-))=(5.945 +/- 0.067 +/- 0.042)% and B(J/psi ->mu(+)mu(-))=(5.960 +/- 0.065 +/- 0.050)%, leading to an average of B(J/psi -> l(+)l(-))=(5.953 +/- 0.056 +/- 0.042)% and a ratio of B(J/psi -> e(+)e(-))/B(J/psi ->mu(+)mu(-))=(99.7 +/- 1.2 +/- 0.6)%, all consistent with, but more precise than, previous measurements.
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