A 2D transform and its inverse have an implementation as a sequence of lifting steps arranged for reduced computational complexity (i.e., reducing a number of non-trivial operations). This transform pair has energy compaction properties similar to the discrete cosine transform (DCT), and is also lossless and scale-free. As compared to a separable DCT transform implemented as 1D DCT transforms applied separably to rows and columns of a 2D data block, the transforms operations are re-arranged into a cascade of elementary transforms, including the 2.times.2 Hadamard transform, and 2.times.2 transforms incorporating lifting rotations. These elementary transforms have implementations as a sequence of lifting operations.