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Non-negative matrix factorization (NMF) has been introduced into the field of hyperspectral unmixing in the last ten years. To relieve the non-convex problem of NMF, different constraints are imposed on NMF. In this paper, a new constraint, termed the endmember dissimilarity constraint (EDC), is proposed. The proposed constraint can measure the difference between the signatures as well as constrain the signatures to be smooth. A set of smooth spectra contained in the dataset space with the largest differences can be obtained, as far as is possible, which can be seen as endmembers. The experimental performances of our method and other state-of-the-art constrained NMF algorithms were obtained and analyzed, proving that the proposed method outperforms other NMF unmixing methods.