  The non-renormalization theorem of chiral vertices and the generalized
non-renormalization theorem of the photon self energy are derived in SQED on
the basis of algebraic renormalization. For this purpose the gauge coupling is
extended to an external superfield. This extension already provides detailed
insight into the divergence structure. Moreover, using the local supercoupling
together with an additional external vector multiplet that couples to the axial
current, the model becomes complete in the sense of multiplicative
renormalization, with two important implications. First, a Slavnov--Taylor
identity describing supersymmetry, gauge symmetry, and axial symmetry including
the axial anomaly can be established to all orders. Second, from this
Slavnov-Taylor identity we can infer a Callan-Symanzik equation expressing all
aspects of the non-renormalization theorems. In particular, the gauge
$\beta$-function appears explicitely in the closed form.
