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A new algorithm for direction-of-arrival (DOA) estimation of non-Gaussian sources is proposed. Based on the joint diagonalization structure of multiple fourth-order cumulant matrices, a novel cost function is designed and a new spatial spectrum for direction finding at hand is derived. Unlike the subspace-based techniques, it is not necessary to determine the number of sources in advance for the proposed algorithm. Moreover, the proposed method is insensitive to the spatially correlated noise. Simulation results are provided to demonstrate the performance of the proposed approach.