  We recalculate the chiral anomaly in the Abelian gauge model in which a
spin-$\frac{1}{2}$ field is directly coupled to a Rarita-Schwinger
spin-$\frac{3}{2}$ field, using the extended theory in which there is an exact
fermionic gauge invariance. Since the standard gauge fixing and ghost analysis
applies to this theory, the ghost contribution to the chiral anomaly is $-1$
times the standard chiral anomaly for spin-$\frac{1}{2}$. Calculation of the
fermion loop Feynman diagrams contributing to the coupled model anomaly gives a
result of $6$ times the standard anomaly, so the total anomaly is $5$ times the
standard anomaly. This agrees with the result obtained from the unextended
model taking the ghost contribution there as $0$, corresponding to a
non-propagating ghost arising from exponentiating the second class constraint
determinant, together with the fermion loop anomaly contribution in the
unextended model of $5$ times the standard anomaly.
