In this study, we investigate the estimation of the Two-Dimensional (2D) Direction Of Arrival (DOA) in monostatic multiple-input-multiple-output radar with cross array and propose a novel, highly accurate DOA estimation method based on unitary transformation. First, we design a new unitary matrix using the central symmetry of a cross array at transmit and receive sites. Then, the rotational invariance relationships of these arrays with long and short baselines can be transformed into a real-value field via unitary transformation. In addition, non-ambiguous and highly accurate 2D DOA estimations can be obtained using a unitary dual-resolution ESPRIT algorithm. Simulations show that the proposed method can estimate 2D highly accurate spatial angles using automatic pairing without incurring the expense of array aperture and peak searching. Compared with traditional unitary transformation, the steering vectors of transmit and receive arrays can be transformed into real-value fields via the unitary matrix and the transformation method of our scheme, respectively. This effectively overcomes the problem of shift invariance factors in real-value fields that cannot be extracted using traditional algorithms. Therefore, the proposed method can absolutely compute eigenvalue decomposition and estimate parameters in a real-value field, resulting in lower computational complexity compared with traditional methods. Simulation results verify both the correctness of our theoretical analysis and the effectiveness of the proposed algorithm.