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Classification of high-dimensional data generally requires enormous processing time. In this paper, we present a fast two-stage method of support vector machines, which includes a feature reduction algorithm and a fast multiclass method. First, principal component analysis is applied to the data for feature reduction and decorrelation, and then a feature selection method is used to further reduce feature dimensionality. The criterion based on Bhattacharyya distance is revised to get rid of influence of some binary problems with large distance. Moreover, a simple method is proposed to reduce the processing time of multiclass problems, where one binary SVM with the fewest support vectors (SVs) will be selected iteratively to exclude the less similar class until the final result is obtained. Experimented with the hyperspectral data 92AV3C, the results demonstrate that the proposed method can achieve a much faster classification and preserve the high classification accuracy of SVMs.