A fractal coding is discussed that concentrates on relieving excessive computation burden and improving image quality in encoding. But the convergence speed of the decoder is important because, in many applications, the encoding is done once, while the decoding is to be repeated many times. Because the well-known fractal coding scheme is based on the iterated function system (IFS), we cannot avoid the iterated transformation though the scheme can be done noniteratively in a special case. Such a transformation encounters difficulty in parallel processing and hence a fast decoding algorithm is necessary. An algorithm to speedup the decoding process is described. The analysis and the simulation results of the proposed method show that our algorithm is much faster than the conventional method.