In a recent paper, we modified the Bilow's diffracted current basis function both within and outside the transition regions to solve the problem that the combined moment method (MM)-physical optics (PO) approach proposed by Bilow fails for some cases. The two expressions are discontinuous when the wedge face is going from outside the transition region to within the transition region. Then, the previous procedure yields nontrivial errors when the transition region is approaching the wedge face. Uniform expressions for the diffracted currents on the wedge surface are derived in this paper.