Recently, the 2q-MUSIC (q ≥ 2) direction finding algorithm has been developed for non-Gaussian sources and square arrangements of the 2qth-order data statistics, to overcome the main limitations of MUSIC and to improve the performance of 4-MUSIC for multiple sources. To further improve the performance of the 2q-MUSIC algorithm, the purpose of this paper is to extend the latter to rectangular arrangements of the data statistics, giving rise to rectangular 2q-MUSIC algorithms. It is shown in particular that rectangular arrangements of the higher order (HO) data statistics allow to optimize the compromise between performance and maximal number of sources to be processed. Besides, it also allows a complexity reduction for a given level of performance. These results, completely new, should open new perspectives for HO array processing.