  A systematic method is given for obtaining consistent approximations to the
Schwinger-Dyson(SD) and Bethe-Salpeter(BS) equations which maintain the
external gauge invariance. We show that for any order of approximation to the
SD equation there is a corresponding approximation to the BS equations such
that the solutions to those equations satisfy the Ward-Takahashi identities of
the external gauge symmetry. This formulation also clarifies the way how we can
calculate the Green functions of current operators in a consistent manner with
the gauge invariance and the axial anomaly. We show which type of diagrams for
the $\pi^0\rightarrow\gamma\gamma$ amplitude using the pion BS amplitude give
result consistent with the low-energy theorem. An interesting phenomenon is
observed in the ladder approximation that the low energy theorem is saturated
by the zeroth order terms in the external momenta of the pseudoscalar BS
amplitude and the vector vertex functions.
