  A few years ago, we found the supersymmetric(SUSY) counterpart of the
spectral triple which specified noncommutative geometry(NCG). Based on "the
triple", we considered the SUSY version of the spectral action principle and
had derived the action of super Yang--Mills theory, minimal supersymmetric
standard model, and supergravity. In these theories, we used vector notation in
order to express a chiral or an anti-chiral matter superfield. We also
represented the NCG algebra and the Dirac operator by matrices which operated
on the space of matter field. In this paper, we represent the triple in the
superspace coordinate system $(x^\mu,\theta,\bar{\theta})$. We also introduce
"extracting operators" and the new definition of the supertrace so that we can
also investigate the square of the Dirac operator on the Minkowskian manifold
in the superspace. We finally re-construct the super Yang--Mills theory on NCG
in the superspace coordinate to which we are familiar to describe SUSY
theories.
