A search for the nonconservation of lepton flavor number in the decay τ±→μ±γ has been performed using 2.07×10^8 e+e-→τ+τ- events produced at a center-of-mass energy near 10.58 GeV with the BABAR detector at the PEP-II storage ring. We find no evidence for a signal and set an upper limit on the branching ratio of B(τ±→μ±γ)<6.8×10^-8 at 90% confidence level.
