  Introduction of supersymmetry into the noncommutative geometry is
investigated. We propose a new Dirac operator which plays the role of the
metric over the extended algebra of chiral and antichiral supermultiplets and
is invariant under the supersymmetry transformations. Inner automorphisms for
the algebra generate vector supermultiplets as an internal fluctuation of the
metric. We show that the supersymmetric QCD action for these supermultiplets is
correctly given by the spectral action principle.
