  We propose a model for radiatively generating the hierarchy of the Standard
Model (SM) fermion masses: tree-level top quark mass; 1-loop bottom, charm, tau
and muon masses; 2-loop masses for the light up, down and strange quarks as
well as for the electron; and 4-loop masses for the light active neutrinos. Our
model is based on a softly-broken $S_{3}\times Z_{2}$ discrete symmetry. Its
scalar sector consists only of one SM Higgs doublet and three electrically
neutral SM-singlet scalars. We do not need to invoke either electrically
charged scalar fields, or an extra $SU_{2L}$ scalar doublet, or the spontaneous
breaking of the discrete group, which are typical for other radiative models in
the literature. The model features a viable scalar dark matter candidate.
