A new algorithm to solve the fused complex-valued cost function for approximate joint diagonalization (AJD), named CVAJD (Complex-Valued Approximate Joint Diagonalization), is presented. The CVAJD algorithm adopts an iterative scheme to update the demixing matrix through the strictly diagonally-dominant residual mixing matrix obtained in each of iterations. Due to the relaxation of several constraints on the target matrices, it has more general utilizations. Besides, it is also easy to implement. A numerical simulation illustrates fast convergence and good performance of the CVAJD.