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This paper presents a simple but high resolution two-dimensional (2-D) direction-of-arrival (DOA) estimation method using second-order partial-differential of MUSIC spectrum. Multiple signal classification (MUSIC) method is paid attention as one of "superresolution" DOA estimation methods because of their brilliant characteristics, however MUSIC also has the problem of estimation accuracy in severe environments like low SNR, small number of snapshots, or incident waves from close angles. Paying attention to the fact that the second-order differential of MUSIC spectrum makes peaks around the original DOAs even when MUSIC spectrum does not make peaks there, we have already presented an accurate one-dimensional (1-D) DOA estimation method that employs the second-order differential of the MUSIC spectrum. In this paper, we develop the previous 1-D second-order differential approach to correspond to 2-D DOA estimation problem and see if it also works for higher dimensional case. The performance of the present method is evaluated in comparison with 2-D MUSIC method through computer simulation.