In this study, a new algorithm for canceling a MRI artifact due to the translational motion In the image plane is described. Unlike the conventional iterative phase retrieval algorithm, in which there is no guarantee for the convergence, a direct method for estimating the motion is presented. In previous approaches, the motions in the x(read out) direction and the y(phase encoding) direction were estimated simultaneously. However, the feature of x and y directional motions are different from each other. By analyzing their features, each x and y directional motion is canceled by the different algorithms in two steps. First, it is noticed that the x directional motion corresponds to a shift of the x directional spectrum of the MRI signal, and the non-zero area of the spectrum just corresponds to the projected area of the density function on the x axis. So the motion is estimated by tracing the edges between non-zero area and zero area of the spectrum, and the x directional motion is canceled by shifting the spectrum in an reverse direction. Next, the y directional motion is canceled by using a new constraint condition, with which the motion component and the true image component can be separated. This algorithm is shown to be effective by using a phantom image with simulated motion.