We report a measurement of the branching fraction of B^+ -> tau^+ nu_tau decays using a data sample of 772 x 10^6 BBbar pairs, collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. We reconstruct the accompanying B meson in a semileptonic decay and detect the recoiling B candidate in the decay channel B^+ -> tau^+ nu_tau. We obtain a branching fraction of BR(B^+ -> tau^+ nu_tau) = [1.25 +- 0.28 (stat.) +- 0.27 (syst.)] x 10^-4. This result is in good agreement with previous measurements and the expectation from the calculation based on the Standard Model.
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