In fractal decoding procedures, the reconstructed image is obtained by means of a predefined number of iterations with an arbitrary initial image. A novel fast decoding algorithm with convergence criteria is proposed. It is composed of a selective decoding of range blocks with a block convergence criterion (BCC), estimation of an initial image, and one-buffer decoding. In the proposed algorithm, continuation of the decoding process is judged by an image convergence criterion (ICC), not by the predefined number of iterations. Without redundant iterations and loss of quality, the reconstructed image is obtained by the amount of calculations corresponding to only three to four iterations of the general decoding procedure.