In this paper, we propose an alternative algorithm, which is faster and more stable, for geometrically constrained independent vector analysis (GC-IVA) to tackle multichannel speech separation problem. GC-IVA is a method that combines IVA, a blind source separation method, with beamforming-based geometrical constraints, which are defined using the spatial information of the sources, so that it allows us to achieve high separation performance while able to obtain the target speech at the desired output channel. GC-IVA with auxiliary-function approach and vectorwise coordinate descent (GCAV-IVA) is one such method, which has the advantage that no step-size tuning is required, the objective function monotonically decreases, and the algorithm converges fast. However, this method requires matrix inversion, which is computationally expensive and adversely affects numerical stability. To address this problem, we propose an algorithm by using the recently introduced iterative source steering (ISS), which uses a sequence of rank-1 update. ISS does not require matrix inversion and achieves a lower computational complexity per iteration of quadratic in the number of microphones, resulting in the proposed method being faster and more stable than GCAV-IVA. The experimental results revealed that the proposed method had higher source separation performance and shorter execution time than conventional methods.