In this paper, we propose a new fractal image decoding algorithm with fast convergence speed by using the data dependence and the improved initial image estimation. Conventional method for fractal image decoding requires high-degrdd computational complexity in decoding process, because of iterated contractive transformations applied to whole range blocks. On proposed method, Range of reconstruction imagte is divided into referenced range and data dependence region. And computational complexity is reduced by application of iterated contractive transformations for the referenced range only. Data dependence region can be decoded by one transformations when the referenced range is converged. In addition, more exact initial image is estimated by using bound () function in case of all, and an initial image more nearer to a fixed point is estimated by using range block division estimation. Consequently, the convergence speed of reconstruction iamge is improved with 40% reduction of computational complexity.