A search is performed for the lepton number violating decay B + → h − μ + μ + , where h − represents a K − or a π − , using an integrated luminosity of 36     pb − 1 of data collected with the LHCb detector. The decay is forbidden in the standard model but allowed in models with a Majorana neutrino. No signal is observed in either channel and limits of B ( B + → K − μ + μ + ) < 5.4 × 10 − 8 and B ( B + → π − μ + μ + ) < 5.8 × 10 − 8 are set at the 95% confidence level. These improve the previous best limits by factors of 40 and 30, respectively.