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Direction of arrival (DOA) estimation for coprime multiple-input multiple-output radar is studied, and a combined unitary estimation of signal parameters via rotational invariance technique (ESPRIT)-based algorithm is proposed. The transmitter and the receiver adopt coprime arrays, which are sparse but still uniform. Therefore, unitary ESPRIT is first used to obtain arbitrary ambiguous DOA estimations based on the rotational invariances of transmit and receive arrays, respectively. After recovering all the other estimations, unique DOA estimation is achieved by finding the coincide results from transmit and receive arrays based on the coprimeness. The proposed algorithm obtains more accurate DOA estimation, achieves higher angle resolution, and identifies more targets than conventional methods. Multiple simulations are conducted to verify the improvement of the proposed algorithm.