  In the present paper we evaluate the anomaly for the abelian axial current in
a non abelian chiral gauge theory, by using dimensional regularization. This
amount to formulate a procedure for managing traces with more than one
$\gamma_5$. \par The suggested procedure obeys Lorentz covariance and
cyclicity, at variance with previous approaches (e.g. the celebrated 't Hooft
and Veltman's where Lorentz is violated) \par The result of the present paper
is a further step forward in the program initiated by a previous work on the
traces involving a single $\gamma_5$. The final goal is an unconstrained
definition of $\gamma_5$ in dimensional regularization. Here, in the evaluation
of the anomaly, we profit of the axial current conservation equation, when
radiative corrections are neglected. This kind of tool is not always exploited
in field theories with $\gamma_5$, e.g. in the use of dimensional
regularization of infrared and collinear divergences.
