  We present an extension of the Standard Model (SM) without supersymmetry,
which we use to calculate order of magnitude values for the elements of the
mass matrices in the SM. In our model we can fit the 9 quark and lepton masses
and 3 mixing angles using only 3 free parameters, with the overall mass scale
set by the electroweak interaction. The specific model described here has the
anti-grand unified gauge group SMG^3 x U(1)_f at high energies where SMG =
SU(3) x SU(2) x U(1) is the SM gauge group. The SM fermions are placed in
representations of the full gauge group so that they do not produce any
anomalies.It is pointed out that the same results can be obtained in an anomaly
free SMG x U(1)^3 model.
