  The scotogenic model of neutrino mass is modified so that the dark Majorana
fermion singlet $S$ which makes the neutrino massive is itself generated in one
loop. This is accomplished by having $Z_6$ lepton symmetry softly broken to
$Z_2$ in the scalar sector by a unique quadratic term. It is shown that $S$ is
a viable freeze-in dark-matter candidate through Higgs decay.
