In this paper, we propose a new algorithm that can decode iterated function system (IFS) codes and is very suitable for parallel implementation of hardware. The initial points used in random iteration algorithm for each contractive affine transformation can be easily determined and hence no transient points are occurred. On the other hand, there are no additional computation and random number generators required in our algorithm. Moreover, the proposed algorithm shows the compatibility that it can be applied to the serial decoding algorithm to obtain a parallel configuration. Computer simulation shows that the proposed algorithm is very efficient and powerful for decoding a fractal image.