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In this paper, a new algorithm for striping noise reduction in hyperspectral images is proposed. The new algorithm exploits the orthogonal subspace approach to estimate the striping component and to remove it from the image, preserving the useful signal. The algorithm does not introduce artifacts in the data and also takes into account the dependence on the signal intensity of the striping component. The effectiveness of the algorithm in reducing striping noise is experimentally demonstrated on real data acquired both by airborne and satellite hyperspectral sensors.