Accurate and fast data unmixing is key to most applications employing hyperspectral data. Among the large number unmixing approaches, Blind Source Separation (BSS) has been employed successfully through a variety of techniques, yet most of these approaches continue to be computationally expensive due to their iterative nature. In this context, it is imperative to seek efficient approaches that leverage the accuracy of the algorithms and the availability of off-the-shelf computationally performant systems such as multi-cpu and multi core. In this paper we tackle the spatial complexity based unmixing, a new technique shown to outperform many BSS solutions. We develop a new parallel algorithm that, without decreasing the accuracy ensures significant computational speedup when compared to the original technique. We provide a theoretical analysis on its equivalency with the algorithm. Furthermore we show through both complexity analysis and experimental results that the algorithm provides a speedup in execution linear to the number of computing cores used.