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Endmember extraction is a key step in the hyperspectral image analysis process. The keel new simplex growing algorithm (KNSGA), recently developed as a nonlinear alteative to the simplex growing algorithm (SGA), has proven a prom-ising endmember extraction technique. However, KNSGA still suffers from two issues limiting its application. First, its random initialization leads to inconsistency in final results; second, excessive computation is caused by the iterations of a simplex volume calculation. To solve the first issue, the spatial pixel purity index (SPPI) method is used in this study to extract the first endmember, eliminating the initialization dependence. A novel approach tackles the second issue by initially using a modified Cholesky fac-torization to decompose the volume matrix into triangular matrices, in order to avoid directly computing the determinant tauto-logically in the simplex volume formula. Theoretical analysis and experiments on both simulated and real spectral data demon-strate that the proposed algorithm significantly reduces computational complexity, and runs faster than the original algorithm.