  We consider the general ${\cal N}=1$ supersymmetric gauge theory with matter,
regularized by higher covariant derivatives without breaking the BRST
invariance, in the massless limit. In the $\xi$-gauge we obtain the
(unrenormalized) expression for the two-point Green function of the quantum
gauge superfield in the one-loop approximation as a sum of integrals over the
loop momentum. The result is presented as a sum of three parts: the first one
corresponds to the pure supersymmetric Yang--Mills theory in the Feynman gauge,
the second one contains all gauge dependent terms, and the third one is the
contribution of diagrams with a matter loop. For the Feynman gauge and a
special choice of the higher derivative regulator in the gauge fixing term we
analytically calculate these integrals in the limit $k\to 0$. In particular, in
addition to the leading logarithmically divergent terms, which are determined
by integrals of double total derivatives, we also find the finite constants.
