  We have measured the process B+- --> (K*+- --> K+- pi0) pi0 based on 232
million Y(4S) --> BBbar decays collected with the BaBar detector at the PEP-II
asymmetric-energy B Factory at SLAC. From a signal yield of 89 +- 26 events we
obtain the branching fraction BR(B+- --> K*+- pi0)=[6.9 +- 2.0 (stat) +- 1.3
(syst)] x10^-6 with a statistical significance of 3.6 standard deviations
including systematic uncertainties, and a charge asymmetry of 0.04 +- 0.29
(stat) +- 0.05 (syst).
