Based on factorization of the transform matrix in triangular elementary reversible matrices (TERM), an integer approximation algorithm of the principal component transform (IPCT) is proposed. We improve the pivoting method of TERM factorization in order to obtain limited error and enhanced computational efficiency, and we develop a new lossless compression algorithm for hyperspectal imagery combining the perfectly reversible integer PCT with the 3-D Tarp coder. After applying an integer wavelet transform in spatial domain we use the improved IPCT for interband derecolation. In coding stage the novel 3-D Tarp coder allows probability estimation with five simple recursive filters. And this probability estimate can be used to drive a non-adaptive arithmetic coder to entropy code significance-map and refinement information of transformed coefficients. The main advantage of our compression algorithm is low complexity and it can yield embedded bitstreams with higher compression ratio compared to existing algorithms.