  We calculate quark and lepton masses and quark mixing angles in the framework
of a supersymmetric SU(4)$\otimes$SU(2)$_L\otimes$SU(2)$_R$ model where the
gauge group is broken at 10$^{16}$ GeV. The model predicts third family
top-bottom-tau Yukawa unification, as in minimal SO(10). The other smaller
Yukawa couplings are assumed to arise from non-renormalisable operators
suppressed by powers of some heavy scale. We perform a systematic operator
analysis of the model in order to find the minimum set of operators which
describe the low energy quark and lepton masses, and quark mixing angles
consistent with low-energy phenomenology. A novel feature of the model is the
possibility of asymmetric texture zeroes in the Yukawa matrices at the scale of
the new physics. Successful predictions are obtained for $m_t$, $\tan \beta$,
$m_s/m_\mu$, $m_d/m_e$ and $V_{ub}$ in terms of a CP violating phase $\phi$.
For example, we predict $\tan \beta = 35-65$, $m_t = 130 - 190$ GeV, and
$|V_{ub}|>0.0040$.
