  We consider an abelian gauge theory with spontaneously broken symmetry
containing a scalar-fermion coupling which is non-linear in the Higgs field.
Although in the unitary gauge it reduces to a pure Yukawa term, suggesting that
the theory is renormalizable, the one loop divergence structure in this gauge
in the fermion-fermion elastic scattering amplitude shows this is not so.
Comparison is made with the theory with a conventional coupling, for which
cancellation of the non-renormalizable divergences occurs.
