In this paper, we propose a method of regional search for fractal image compression and decompression. In this method, the search for fractal codes is carried out in a region of the image instead of over the whole image. Because the area surrounding a partitioned block has a high probability of being similar to the block, the use of regional search to find the fractal codes results in sharply reduced compression times with only minor increases in the compression ratio, as compared to conventional methods. By using a 128x128 search region, we can compress a 1024x1024 Lena image on a Pentium II-300 PC in 2.8 seconds, obtaining results of high visual quality, with a compression ratio of 87 and a PSNR of 36.67. By comparison, conventional fractal image compression requires 176 seconds, has a compression ratio of 84 and has a PSNR of 39.68. Moreover, if we reduce the search regions to 32x32 and accept a slightly more basic level of visual quality, the compression time is 1.0 second, the compression ratio is 91 and the PNSR is 33.98.