  In a model with a gauge group $G_{SM}\otimes U(1)_X$, where $G_{SM} \equiv
SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$ is the standard model gauge group and
$U(1)_X$ is a horizontal local gauge symmetry, we propose a radiative
generation of the spectrum of quark masses and mixing angles. The assignment of
horizontal charges is such that at tree level only the third family is massive.
Using these tree level masses and introducing exotic scalars, the light
families of quarks acquire hierarchical masses through radiative corrections.
The rank three quark mass matrices obtained are written in terms of a minimal
set of free parameters of the model, whose values are estimated performing a
numerical fit. The resulting quark masses and CKM mixing angles turn out to be
in good agreement with the experimental values.
