We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation ()<sup> <i></i>/2</sup>, 0 < <i></i> 1). We show in this paper that if , or with is a weak solution of the 2D quasi-geostrophic equation, then <i></i> is a classical solution in . This result improves our previous result in [18].