In this paper, a best-basis selection algorithm that improves the performance of the coding gains and the computational complexity is proposed. The proposed algorithm limits the computational complexity according to the resolved threshold value and decomposes the parent subbands by using the top-down tree search and the relative energy between the parent subbands and the child subbands. For the experiments of the proposed algorithm, the bit-rates, the peak signal-to-noise ratio (PSNR), and the reconstructed images are presented by using the Quad-tree coder. The result of the proposed algorithm is compared to that of DWT algorithm using the Quad-tree coder for a set of standard test images. In addition, the result of the proposed algorithm is compared to that of JPEG-2000 algorithm and that of S+P algorithm.