A fast CayleyMenger determinantbased endmember extraction algorithm for hyperspectral unmixing was proposed. The algorithm is to find the simplex enclosing the hyperspectral data with minimum volume. It improves current simplexbased algorithms in several aspects. The introduction of CayleyMenger determinant makes it easy to use features of Hermite matrix to accelerate the searching process and gives a stable result finally. Moreover, a dimensionality reduction transform is not necessary in this algorithm, which will avoid the loss of useful information during the dimensionality reduction. The experimental results on synthetic and real hyperspectral dataset demonstrated that the proposed algorithm is a fast and accurate algorithm for the hyperspectral unmixing.