  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$_t$.
