  We first confirm that Nishijima's method of the $\pi^0 \rightarrow \gamma
+\gamma $ calculation can precisely reproduce the observed life time of $\pi^0$
decay. Then, we calculate, for the first time, the T-matrix of the $Z^0
\rightarrow \gamma +\gamma $ process in which the vertex of the $\gamma^\mu
\gamma_5$ is responsible for the decay of the weak vector boson. Even though
the decay rate itself vanishes to zero due to the symmetry nature of two
photons (Landau-Yang theorem), the T-matrix of the process has neither linear
nor logarithmic divergences. Therefore, there is no room for the regularization
of the triangle diagrams with the $\gamma^\mu\gamma^5$ vertex. Further, the
T-matrices of all the triangle diagrams do not have any divergences at all, and
therefore it is rigorously proved that the anomaly equation is spurious and
appears only because of the improper regularization of unphysical amplitudes.
