Preprint IHEP IHEP IHEP 2005-20, hep-ex/0506023 Authors: O.Tchikilev, et al. "Observation of the radiative kaon decay K- --> mu-pi0gammanu" Abstract Using data collected with the ISTRA+ spectrometer during the 2001 run of the U-70 proton synchrotron in Protvino, we report the first observation of the radiative kaon decay K- -->mu-pi0gammanu. We find Br(Kmu3g)/Br(Kmu3) for two regions 5