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Hyperspectral image's vast data volume brings about many problems in data processing. It also comes at a price that such wealthy spectral information is highly correlated. Selection of optimal bands is an effective means to mitigate the curse of dimensionality for remote sensing data. In this paper, we propose a new inter-class separability criterion, that is Spectral Separability Index, and present a band selection algorithm for hyperspectral image classification. We take three factors which include the amount of information, inter-class separability and band correlativity into consideration. The experiments show that the result of our algorithm is better than Euclidean Distance, Spectral Angle Mapper, and Spectral Correlation Mapper algorithm.