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Many blind source separation algorithms only try to find the estimation of original signals and the de-mixing system. However, finding the mixing system is also an important task, which is a representation for the recording environment. Direct inversing the mixing system will introduce many noises. We proposed a correlation based backward-forward combined algorithm to do blind source separation. In the proposed algorithm, an alternative optimization strategy is applied. The estimation of mixing/de-mixing system is used as an initial guess to optimize the de-mixing/mixing system iteratively. This alternative optimization algorithm can obtain better estimation for mixing and de-mixing system at the same time. In addition, it can reduce the chance to be tracked into a local minimal. As a result, we can get a better estimation for the sources. Good experimental results were obtained on both simulated and real signals.