Remote sensing produces large amounts or digital data which are collected into databases. Since a variety of applications utilize the multispectral data, the data cannot be compressed with lossy methods. In this paper, we propose the combination of two reversible methods for the lossless compression of the multispectral images: first, principal component analysis is applied to the spectra of the image and then, the integer wavelet transform is applied to the residual image to further concentrate the energy and reduce the entropy. The coding quality of the method is measured with the the zero-order entropy, and it is clearly lower with this method than with the methods found from the literature. Depending on the AVIRIS image, the entropies varied from 5.6 to 5.9 bits per pixel. With the same images, the actual compression ratios, calculated from the files sizes, were in the range from 2.8 to 2.9.