  We consider super Yang-Mills Theory in $N=1$ conformal supergravity. Using
the background field method and the Feddeev-Popov procedure, the quantized
action of the theory is presented. Its one-loop effective action is studied
using the heat kernel method. We shall develop a non-iterative scheme,
generalizing the non-supersymmetric case, to obtain the super heat kernel
coefficients. In particular, the first three coefficients, which govern the
one-loop divergence, will be calculated. We shall also demonstrate how to
schematically derive the higher order coefficients. The method presented here
can be readily applied to various quantum theories. We shall, as an
application, derive the full one-loop divergence of SYM in conformal
supergravity.
