We discuss the conventional chiral Schwinger model with the minimal Wess-Zumino action. The Schwinger term between Gauss-law constraints G(x) and G(y) can not be cancelled by the minimal Wess-Zumino action. If we define a modified Gauss-law constraint G_M(x), the Schwinger term between the constraints G_M(x) and G_M(y) disappear. The full action is gauge invariant. When we pick the unitary gauge theta =0, the chiral Schwinger model with the generalized Faddeevian regularization scheme is obtained. The relation between Faddeevian and usual regularization can also be established.