The inner product of digital comp ressing technique (DCT) coefficients is defined which is equal to the inner product of spatial coefficients. It can be judged as close matches. The relationship is induced between indentity transformation and the rest transformations on DCT domain. The range block is separated into three classes∶steady,middle and active. The relationship between the nubmer of low frequency coefficients and the quality of decoded image i s analyzed. The algorthm of fractal image encoding is proposed based on the inner product ofDCT coefficients and local variance. The algorithm is compared with that in literature [ 2 ] and [ 3 ]. Experiments show that the speed can be improved greatly with the ensurance of the decoded image quality.