||A new decoding technique based on an iterative method with pixel updating is proposed for fractal image compression. We prove that the new iterative method converges in the most general case of variable shape segmentations, unconstrained domains, and use of pixel shuffling. We show that in some important cases the new method has a greater rate of convergence than the conventional method. Furthermore, it is indicated how standard iterative methods can be efficiently implemented in fractal image compression. Finally, experimental results confirming the superiority of our technique are presented.