The conventional decoding procedure for the images encoded using fractal contractive transformation algorithms is performed by applying the transformations iteratively for an arbirary initial image. In this paper, we showed that the atractor image can be obtained analytically when the image is encoded using the fractal algorithm proposed by Monro and Dudbridge, in which the corresponding domain block for a range block is fixed. Using the analytical formula, we can obtain the attractor image without iteration procedure. Computer simulation results for various test images show that we can increase the image decoding speed by more than five times when we use the analytical formula compared to the previous iteration methods. Also we confirmed that the real time decoding by software on PD is possible for the moving picture with QCIF formats.