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The joint diagonalization technique is an important type of method for blind source separation. In this paper, a new approach is presented to joint diagonalization for a set of symmetric matrices with a general (and not necessarily orthogonal) matrix. The approach performs joint diagonalization via a series of symmetric eigen decompositions, including merits of simplicity, effectiveness, and computational efficiency. Simulation results demonstrate the potential improvement of the performance in the context of blind source separation.