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Hyperspectral remote sensing image has the characteristics of hundreds of bands, high relevancy, and high redundancy, which bring difficulties to the further processing task. In order to reduce the dimension, this paper proposes an effective band selection method based on time series analysis of important points. The method takes all the continuous band of hyperspectral remote sensing images as time series and performs K-means clustering based on the DBI criterion firstly, then the cluster centers undergo wavelet filtering, and finally important points of the time series curves are extracted and merged as the basis for band selection. To verify the effectiveness of the proposed method, classification using SVM classifier is conducted on the reduced spectral images. The results show that the proposed band selection methods with important points based on time series analysis can choose those bands with discriminative information, and it can achieve dimension reduction rate close to 90%. Compared with other state-of-the-art methods, the presented method is competitive with a lower computational complexity, while maintaining a higher classification accuracy at the same time.