  In this paper we consider a variation of the Vafa-Witten equations on
compact, oriented and smooth 4-manifolds, and construct a set of perturbation
terms to establish the transversality of that equations. The new perturbed
equations provide us a priori estimates of the solutions, while the original
reduced Vafa-Witten equations does not. By applying the a priori estimates we
show that the singular of the solutions can be removed, and then construct the
Ulhenbeck closure of the moduli spaces.
