This paper presents a new independency metric for blind source separation (BSS) problem. It is mathematically proved that the metric value of any linear combination of source signals is less than the largest one of sources under a loose condition. Further, the global optimization of this new metric is achieved by formulating it as a generalized eigenvalue problem. Subsequently, we guarantee to find out a correct de-mixing matrix through maximizing the proposed metric to separate the sources. The simulation results have shown its success in separating the linear combinations of sub-Gaussian and super-Gaussian sources with at most one Gaussian signal. KEY WORDS Blind Source Separation, Independency Metric, Independent Component Analysis, Generalized Eigenvalue Problem, Global Optimization.