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We report the results of a search for the rare, purely leptonic decay B−→μ−ν¯μ performed with a 711 fb−1 data sample that contains 772×106 BB¯ pairs, collected near the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e− collider. The signal events are selected based on the presence of a high momentum muon and the topology of the rest of the event showing properties of a generic B-meson decay, as well as the missing energy and momentum being consistent with the hypothesis of a neutrino from the signal decay. We find a 2.4 standard deviation excess above background including systematic uncertainties, which corresponds to a branching fraction of B(B−→μ−ν¯μ)=(6.46±2.22±1.60)×10−7 or a frequentist 90% confidence level interval on the B−→μ−ν¯μ branching fraction of [2.9,10.7]×10−7.