A very simple extension of the Standard Model to include an Abelian fa
mily symmetry is able to describe the hierarchy of quark and lepton ma
sses and their mixing angles together with the unification of gauge co
uplings. We consider the implications of this model for neutrino masse
s and mixing angles and show that they are determined up to a discrete
ambiguity corresponding to the representation content of the Higgs se
ctor responsible for the Majorana mass matrix.