In the last decade, 2q -MUSIC, an extension of MUSIC algorithm to an arbitrary even order 2q, has been proposed to process direction-finding problems. Despite of its better performance compared with MUSIC, it suffers from the high computational complexity, thus limiting its practical application. This letter proposes a method called Non-Redundant-2q-MUSIC using 2qth order statistics for uniform linear arrays and uniform rectangular arrays. The proposed method lowers the computational complexity effectively by removing the redundancy of the virtual array and the 2q th-order cumulant matrix. And root-MUSIC can be applied to avoid calculating the pseudo-spectrum. It is illustrated in both theoretical proof and computer simulations that the proposed method performs properly and effectively.