Abstract: The DOA (Direction of Arrival) estimation for SULA (Sparse Uniform Linear Array) has ambiguity problem. Aiming that, according to the non-linearity between ambiguous directions and array rotation, a rotatory ambiguity cancelling theorem was proved. The theorem reveals that when the element spacing and rotatory angle satisfy certain constraint, the ambiguities before and after the rotation will not overlap in the same coordinate system. Based on the theorem, a MJ-MUSIC (Multiple-Joint MUSIC) method was further proposed for applying on a sparse X-shaped array, which replaces the SULA rotation with its included angle and staggers the ambiguities. By combining the received signals from both arms of the array, the difference between actual peaks and spurious ones can be amplified, which leads to better estimation correct rate. Simulation results demonstrate that the correctness and effectiveness of proposed theorem and MJ-MUSIC method.