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A binaural hearing-aid system based on two-stage blind sound source separation (BSS) method is now being studied by some of the authors. This system consists of two techniques; a single-input multiple-output (SIMO)-model-based independent component analysis part and binaural-output-capable SIMO-model-based binary masking (SIMO-BM) parts. However owing to user-specific head-related transfer function (HRTF) for receiving the sounds and adopting SIMO-BMs in the 2nd stage, the previous system has directivity dependency for sound sourcespsila layout. In this paper, we introduce a new BSS method which mitigates user-specific HRTF and keep the separation performance. The experimental results reveal that the separation performance can be improved by using the proposed method compared with the conventional methods in case of sound sources are located lopsidedly.