hyperspectral images are widely used in real applications due to their rich spectral information. however, the large volume brings a lot of inconvenience, such as storage and transmission. hyperspectral band selection is an important technique to cope with this issue by selecting a few spectral bands to replace the original image. this article proposes a novel band selection algorithm that first estimates the redundancy through analysing relationships among spectral bands. after that, spectral bands are ranked according to their relative importance. subsequently, in order to remove redundant spectral bands and preserve the original information, a maximal linearly independent subset is constructed as the optimal band combination. contributions of this article are listed as follows: (1) a new strategy for band selection is proposed to preserve the original information mostly; (2) a non-negative low-rank representation algorithm is developed to discover intrinsic relationships among spectral bands; (3) a smart strategy is put forward to adaptively determine the optimal combination of spectral bands. to verify the effectiveness, experiments have been conducted on both hyperspectral unmixing and classification. for unmixing, the proposed algorithm decreases the average root mean square errors (rmses) by 0.05, 0.03, and 0.05 for the urban, cuprite, and indian pines data sets, respectively. with regard to classification, our algorithm achieves the overall accuracies of 77.07% and 89.19% for the indian pines and pavia university data sets, respectively. these results are close to the performance with original images. thus, comparative experiments not only illustrate the superiority of the proposed algorithm, but also prove the validity of band selection on hyperspectral image processing.