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A new algorithm for lossless compression of hyperspectral imagery is proposed. First, the average value of four neighbour pixels of the current pixel is calculated as local mean, which is subtracted by the current pixel to eliminate correlation in the current band image. The residual produced by this step is called local difference. The local differences of the pixels which co-locate with the current pixel in previous bands form the input vector of the recursive least square (RLS) filter, by which the prediction value of the current local difference is produced. Then, the prediction residual is sent to the adaptive arithmetic encoder. Experiment results show that the proposed algorithm produces state-of-the-art performance with relatively low complexity, and it is suitable for real-time compression on satellites. Introduction: Hyperspectral imagery produced by imaging instruments on the satellite contains abundant information of the Earth's surface, which leads to overwhelming storage and transmission bandwidth. Compression technology is an efficient solution for those problems. Lossless compression is mandatory in many situations, because hyperspectral imagery is analysed not only by human visual systems, but also by mechanical algorithms. Conventional lossless compression algorithms for red-green-blue images, such as JPEG-lossless (LS) [1], can be applied for hyperspectral imagery. However, these algorithms do not exploit the correlations in the bands of hyperspectral imagery. One of the mentioned algorithms in [2], Diff.JPEG, extends JPEG by applying inter-band prediction between two adjacent bands. Some algorithms exploit the multidimensional property of hyperspectral imagery. In [3], the algorithm called clustered-differential pulse code modulation (C-DPCM) clusters the imagery firstly, and then carries out linear prediction. This algorithm generates a very high compression ratio. However, the cluster step is time-consuming, and this algorithm is too complex for real-time applications. A series of algorithms are put forward in [4] based-on look-up tables (LUTs), which can generate good performance with very low complexity. The performances of LUT-type algorithms for the uncalibrated image are inferior to the fast lossless (FL) algorithm proposed in [2], which has been adopted as the recommended standard of the Consultative Committee for Space Data Systems (CCSDS) for onboard real-time compression of hyperspectral imagery [5]. The FL has significantly lower complexity than IP-3 proposed in [6], although the performance of FL is no better than that of IP-3. In this Letter, we propose a lossless compression algorithm based on a recursive least squares (RLS) filter, which generates state-of-the-art performance with relatively low complexity.