The mass spectrum οίμ⁺μ~γ systems produced in the π ~ ρ interactions at momenta of 25 and 33 GeV/c was investigated. A wide-aperture magnetic spectrometer and a hodoscopic 7-ray detector were used for the recording of muon pairs and γ quanta. A sharp peak corresponding to the η' -+μ ⁺μ ~ γ decay not observed earlier was detected in the mass spectrum. The relative probability of this decay (8 X10 ~⁵) and the spectrum of muon pairs are in agreement with the model of the form factor of the η' meson, which is based on vector dominance.