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The encoding step in a fractal image compression is very time consuming, because a large numbers of sequential search through a list of domains are needed to find the best match for a given range block. Adaptive domain clustering is one solution to overcome this computational burden. The use of a new metric with fewer operations for domain-range blocks comparison is fruitful. In this study, range and domain blocks are categorised by fuzzy c-mean-clustering approach and compared with the use of new metric based on discrete cosine transform coefficient. Experimental results show that by clustering image pixels into five clusters, the encoding step was 8.88 times faster than the full-search method (no clustering) at the expense of some reduction in the decoded image's quality. But the proposed method with the same number of clusters speeds up the encoding process by 45 with lower PSNR decay.