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For fractal image coding, flat range blocks are reconstructed only by their mean pixel values, and non-flat range blocks are reconstructed by the best matching domain blocks that are most similar to the range blocks selected from non-flat domain blocks. So, the threshold values of standard deviation for flat/non-flat range blocks and for flat/non-flat domain blocks influence the quality of the reconstructed image. In this paper, we propose a design method for threshold values of flat/non-flat blocks to obtain a high quality reconstructed image. From the results of simulation experiments, the relationships between the threshold value of flat/non-flat range blocks and of flat/non-flat domain blocks which can produce a high quality reconstructed image is expressed by a proportionality relationship. The approximation error is consequently suppressed to within 0.15 dB. The effectiveness of the proposed method using these threshold values is shown below.