Blind source separation (BSS) aims to estimate unknown sources from their mixtures. Methods to address this include the benchmark ICA, SCA, MMCA, and more recently, a dictionary learning based algorithm BMMCA. In this paper, we solve the separation problem by using the recently proposed SimCO optimization framework. Our approach not only allows to unify the two sub-problems emerging in the separation problem, but also mitigates the singularity issue which was reported in the dictionary learning literature. Another unique feature is that only one dictionary is used to sparsely represent the source signals while in the literature typically multiple dictionaries are assumed (one dictionary per source). Numerical experiments are performed and the results show that our scheme significantly improves the performance, especially in terms of the accuracy of the mixing matrix estimation.