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This letter presents a new endmember generation method, which is called the geometric optimization model (GOM). The algorithm exploits the following fact: an L-dimensional (L-D) simplex can be divided into L + 1 L-D smaller simplexes by any point within the simplex, and the sum of the volumes of the L + 1 smaller simplexes is equal to the volume of the simplex. Based on this geometrical property, we propose a new objective function for endmember generation, whose variable only includes the mixing matrix. As a result, all the problems caused by the abundance matrix can be avoided. Experiments using both simulated and real hyperspectral data show that the GOM is effective in searching the optimal solution.