The reduction of hyperspectral image and multispectral image is an effective task in the domain of compression. The compression technique employed must be reversible inorder to reuse the data further. Several factors make the constraints particularly stringent and the challenge exciting. First is the size of the data: as a third dimension is added, the amount of data increases dramatically making the compression necessary at different steps of the processing chain. Also different properties are required at different stages of the processing chain with variable tradeoff. Second, the differences in spatial and spectral relation between values make the more traditional 3D compression algorithms obsolete. Here the compression of hyperspectral image is proposed with the Discrete Orthonormal Stock-well Transform and Principal Component Analysis (PCA). The PCA algorithm is capable of reduction of dimensionality of the input hyperspectral images with the help of the calculation of Eigen values and Eigen vectors of the input hyper spectral matrix. The algorithm is based on a simple decomposition of the DOST matrix. Conjugate symmetry for the DOST and propose a variation of the parameters that exhibits symmetry, akin to the conjugate symmetry of the FFT of a real-valued signal. Then these orthonormal features formed as an image that is called as feature image. From which original image and feature image, can residual image by subtracting feature image from original image. The residual image and feature image together used for compression of the input hyper spectral image. After that apply PCA algorithm on residual image for obtaining the compressed image. The decompression is performed based on the reversal operation of DOST and PCA. The decompression process is done in stepwise manner first the residual image and then the feature image. Analysis the performance of accuracy and SNR for different classes. The calculated performance values indicates that the proposed method is more efficient compared to the existing works for the compression of the hyper spectral images like JPEG compression in 1D and 2D, Sub PCA in 1D and 2D.