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This letter presents a lossless compression method for ultraspectral sounder data. The method utilizes spectral linear prediction that exploits statistical similarities between different granules. The linear prediction with optimal granule ordering (LP-OGO) method computes linear prediction coefficients using a different granule. That approach requires one to tentatively compress all the other granules one at a time for prediction coefficient computation. The optimal ordering problem of the granules is solved by using Edmonds' algorithm. Our linear prediction with constant coefficients (LP-CC) compression method requires neither tentative compression of all the granules nor optimal ordering of the granules. We randomly select a predetermined number of granules and use that set of granules for computing constant linear prediction coefficients. Those linear prediction coefficients are used in the compression of all the other granules. The results show that the proposed method gives comparable results to the state-of-the-art method, i.e., LP-OGO, on publicly available National Aeronautics and Space Administration Atmospheric Infrared Sounder data. At the same time, the proposed method is practically applicable because it is not computationally prohibitive.