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An effective method is introduced to compensate the effects of mutual coupling for the Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) direction finding algorithm in application of signal snapshot array processing. Changing the covariance matrix into a Teoplitz matrix can achieve high resolution in the Direction Of Arrive (DOA) estimation. How the mutual coupling affects the array antennas has been discussed and a new definition of mutual impedance has been used to characterize the mutual coupling effects between the array elements. Based on the new mutual impedance matrix, a practical method is presented to eliminate the effects of mutual coupling for ESPRIT in the single snapshot data processing. The simulation results show that,this new method not only properly reduces the effects of mutual coupling, but also maintains its steady performance even for weak signals.