This paper presents a new fractal coding scheme to find a suboptimal transformation by performing an iterative encoding process. The optimal transformation can be defined as the transformation generating the closest attractor to an original image. Unfortunately, it is impossible in practice to find the optimal transformation, due to the heavy computational burden. In this paper, however, by means of some new theorems related with contractive transformations and attractors, it is shown that for some specific cases the optimal or suboptimal transformations can be obtained. The proposed method obtains a suboptimal transformation by performing iterative processes as is done in decoding. Thus, it requires more computation than the conventional method, but it improves the image quality. For a simple case where the optimal transformation can actually be found, the proposed method is experimentally evaluated against both the optimal method and the conventional method. For a general case where the optimal transformation is unavailable due to heavy computational complexity, the proposed method is also evaluated in comparison with the conventional method.