The paper presents a new fractal image compression scheme

which merges the range blocks as much as possible in a 4-connected extending way to decrease the amount oI the transformations under a given error tolerance

with a quick searching algorithm. Through rearranging the storing order of the transformations according to their edges

we only need to record their surrounding rectangles for those complicated ranges blocks .whose shape can be recovered using a paint-like rendering method in decoding.Our experiment on Lenna is pleasing.the compression ratio reach 41 at a PNSR of 29.63dB.