Radiative decay of the massive neutrino ni(i) --> nu(j)gamma(m(i) > m(
j)) in a constant crossed electromagnetic field is investigated within
the framework of the standard electroweak theory. It is shown that th
e decay is catalyzed by the external field. This effect becomes signif
icant in a strong crossed field (F much greater than B(e) = m(e)2/e co
ngruent-to 4.41 x 10(13) G) and even more pronounced for the ultrarela
tivistic neutrino (E(nu) much greater than m(nu)) in a relatively weak
field (F much less than B(e)).