This letter discusses the issue of joint angle-of-arrival (AoA) and angle-of-departure (AoD) estimation for multi-input multi-output (MIMO) arrays, so as to conceive a novel one-snapshot multiple signal classification (MUSIC)-derived algorithm based on channel reconstruction therein. Compared to conventional two-dimensional MUSIC (2D-MUSIC), not only does the proposed algorithm avoid the problem of matrix rank deficit, but it also brings a prominent complexity reduction yet achieving satisfactory accuracy. Simulation results verify the utility and advancement of our algorithm, especially in the scheme with high real-time requirements.