In this paper we propose a Multiple-SIgnal- Classification (MUSIC) based algorithm for joint direction finding and delay estimation of the impinging rays in the presence of antenna mutual coupling. We show that with the addition of auxiliary sensors on both sides of the antenna array the algorithm developed earlier can be extended to this scenario. The new algorithm also consists of three stages of the one-dimensional (1- D) MUSIC algorithms which alternatively estimate the impinging directions of arrival (DOAs) and delays in a hierarchical tree structure. Moreover, a constrained temporal filtering process or a constrained spatial beamforming process are employed to partitioned progressively the signals with either close DOAs or close delays into finer subgroups, aiming at higher estimation accuracy and lower computational load. In addition, the developed algorithm proceeds in a tree structure, so the estimated parameters are automatically paired. Conducted simulation results show that the new algorithm provides satisfactory performance but with drastically reduced computations compared with previous work in the presence of mutual coupling.