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Spectral transforms are widely used for the codification of remote-sensing imagery, with the Karhunen-Loêve transform (KLT) and wavelets being the two most common transforms. The KLT presents a higher coding performance than the wavelets. However, it also carries several disadvantages: high computational cost and memory requirements, difficult implementation, and lack of scalability. In this paper, we introduce a novel transform based on the KLT, which, while obtaining a better coding performance than the wavelets, does not have the mentioned disadvantages of the KLT. Due to its very small amount of side information, the transform can be applied in a line-based scheme, which particularly reduces the transform memory requirements. Extensive experimental results are conducted for the Airborne Visible/Infrared Imaging Spectrometer and Hyperion images, both for lossy and lossless and in combination with various hyperspectral coders. The results of the effects on Reed Xiaoli anomaly detection and k-means clustering are also included. The theoretical and experimental evidences suggest that the proposed transform might be a good replacement for the wavelets as a spectral decorrelator in many of the situations where the KLT is not a suitable option.