  We demonstrate that the Standard Model amplitude for $f_1 \bar f_2
\rightarrow W^\pm Z $ at the Born-level exhibits an approximate zero located at
$\cos\theta = (g^{f_1}_{-} + g^{f_2}_{-}) / (g^{f_1}_{-} - g^{f_2}_{-})$ at
high energies, where the $g^{f_i}_{-}$ ($i=1,2$) are the left-handed couplings
of the $Z$-boson to fermions and $\theta$ is the center of mass scattering
angle of the $W$-boson. The approximate zero is the combined result of an exact
zero in the dominant helicity amplitudes ${\cal M}(\pm,\mp)$ and strong gauge
cancelations in the remaining amplitudes. For non-standard $WWZ$ couplings
these cancelations no longer occur and the approximate amplitude zero is
eliminated.
