  The non-renormalization theorems of chiral vertex functions are derived on
the basis of an algebraic analysis. The property, that the interaction vertex
is a second supersymmetry variation of a lower dimensional field monomial, is
used to relate chiral Green functions to superficially convergent Green
functions by extracting the two supersymmetry variations from an internal
vertex and transforming them to derivatives acting on external legs. The
analysis is valid in the massive as well as in the massless model and can be
performed irrespective of properties of the superpotential at vanishing
momentum.
