To solve the target localization problem in a bistatic multiple-input multiple-output (MIMO) radar, a method based on upper-triangularization of the joint matrix is proposed to estimate the direction of departure (DOD) and direction of arrival (DOA). The angle estimation is first transformed to a joint-matrix
upper-triangularization problem. The extended QZ iteration algorithm is then used to solve the problem. The steering matrices of transmission and receiving are estimated. Thus, the DOD and DOA are recovered by spectrum analysis. The proposed method uses the full information in the matched filter output without the need of two-dimensional search for the spectral peaks. It produces an accurate closed form solution in each iteration. Compared with the existent approaches, the proposed method provides better angle estimation accuracy with the DOD and DOA automatically paired. Effectiveness of the method is shown in simulation.