Spectral unmixing is one of the important techniques for hyperspectral data analysis. Full constrained (i.e., non-negative and sum to one constrained) least squares linear spectral mixture modeling (FCLS-LSMM) is widely used for its conciseness and clarity of physical meaning. Unfortunately, the traditional iterative processing for solving FCLS-LSMM is of heavy computational burden. The recently developed geometric analysis method of LSMM provided a new way for decreasing the complexity of LSMM. The unmixing results, however, are not in line with the FCLS requirements. In this case, a new geometric unmixing method is constructed to completely meet the FCLS requirements. The method is of very low complexity and has the capability to obtain the theoretically optimal solution. Experiments show the effectiveness of the proposed method.