[en] The result of the calculation of the charged lepton decay process with flavour violation and emission of two photons l_i^±→± l_J^±γγ in the framework of the standard model with fermion mixing is given. The calculations were performed under the condition that m₂² << m₁² << m_w². It is shown that the ratio of the two-photon and one-photon decay probabilities Br = W^γγ/W^γ is independent of either the mixing angles, or the virtual lepton masses, but depends only on the experimental conditions of the registration of the decay products. (orig.)