Lossless compression is an important topic in ultraspectral sounder data which includes thousands of spectral channels and it needs to store or transmit data in an efficient form. In this paper, a recursive least squares (RLS) based prediction method is proposed for the lossless compression of ultraspectral data. Experiments are performed on 10 granule maps which are acquired by NASA's Atmospheric Infrared Sounder (AIRS) system. The experimental results show that the proposed method provides comparable compression ratios to the-state-of-the-art-methods, i.e., ADQPCA and FSQPCA. Given its compression performance and lower complexity, the proposed method can be effectively implemented to embedded systems and it is well suited for onboard processing on satellites.