Is U(1)${}_H$ a Good Family Symmetry?

We analyze U(1)${}_H$ as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3)${}_c\otimes$SU(2)${}_L\otimes$U(1)${}_Y\otimes$U(1)${}_H$ nonsupersymmetric, are able to fit the experimental result m${}_b<<$m${}_t$.