  In this paper we consider the Vafa-Witten equations on closed, oriented and
smooth 4-manifolds, and construct a set of perturbation terms to establish the
transversality of the perturbed Vafa-Witten equations at the general part of
the solutions. Then we show that for a generic choice of the perturbation
terms, this part of the moduli space for the structure group $SU(2)$ or $SO(3)$
on a closed 4-manifold is a smooth manifold of dimension zero.
