We report the results of a search for the rare, purely leptonic decay B- -> mu(-)(nu) over bar (mu) performed with a 711 fb(-1) data sample that contains 772 x 10(6) B (B) over bar pairs, collected near the Upsilon(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- -> mu(-)(nu) over bar (mu)) = (6.46 +/- 2.22 +/- 1.60) x 10(-7) or a frequentist 90% confidence level interval on the B- -> mu(-)(nu) over bar (mu) branching fraction of [2.9, 10.7] x 10(-7).