The supersymmetric partner of the muon was searched for in a systematic way. No candidate was found and 95% CL limits on its mass were given for different cases. If it is stable, the limit is . If it decays into a muon and an invisible low-mass particle, the limit is . If it decays into a muon and an unstable neutral particle which decays further into a photon and an invisible massless particle, the limit is .