  The radiative decay of the massive neutrino $\nu_i \rightarrow \nu_j \gamma (
m_i > m_j )$ in the external electromagnetic field is analyzed in detail in the
framework of the standard model with lepton mixing. It is shown, that a sort of
a catalysis of the neutrino radiative decay takes place. The effect of
catalysis is significant in the strong electromagnetic fields ($F \gg B_e =
m^2_e / e \simeq 4.41 \cdot 10^{13}$ G) ; it is more pronounced in the case of
the decay of the ultrarelativistic neutrino $(E_{\nu} \gg m_{\nu})$, even in a
relatively weak electromagnetic field ($F \ll m^2_e/e$).
