Among discrete orthogonal transforms, Karhunen-Loeve transform (KLT) achieves the most optimal spectral decorrelation for hyperspectral data compression with minimum mean square error. A common approach for those spectral decorrelation transform techniques such as KLT is to select m coefficient using some threshold value and then treating the rest of the coefficients as zero, this will result in loss of information. In order to preserve more information on small target data, this paper focused on a new technique called joint KLT-Lasso. The Lasso was applied to KLT coefficient. Sparse loadings were obtained using the Lasso constraint on KLT regression coefficients and more coefficients were shrunk to exact zero. The goal of our new method is to introduce a limit on the sum of the absolute values of the KLT coefficients and in which some coefficients consequently become zero without using any threshold value. A simulation on different hyperspectral data showed encouraging results.