Abstract: Strong intra-band correlations along with numerous bands seriously hinder the processing and applications of hyperspectral remote sensing images in realistic applications. A separable non-negative matrix factorization (SepNMF) method is presented to explore the band selection problem on hyperspectral imagery (HSI). The method investigates the separability structure in the band set of the HSI data to improve the regular non-negative matrix factorization model, and it formulates the band selection problem into the problem of finding representative columns that represent other bands with non-negative and linear combinations in the SepNMF model. The method adopts the recursive projection method to iteratively select the representative bands to constitute the proper band subset. Three groups of experiments on two open HSI data sets are designed to carefully testify the performance of the SepNMF in band selection. Several popular methods are utilized to compare against the proposed SepNMF method. Experimental results show that the SepNMF obtains the best overall classification accuracies of all while taking shorter computational times ranking second among all the comparison methods. Therefore, the SepNMF method can be an alternative choice for selecting proper bands in hyperspectral image classification.