A new algorithm for canceling MRI artifact due to 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 proposed. In the previous approach, the motions in the readout (x-) direction and the phase encoding (y-) direction are estimated simultaneously. However, the feature of each x- and y- directional motion is different. By analyzing their features, each x- and y-directional motion is canceled by different algorithms in two steps. First, we notice 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 x-axis projected area of the density function. So the motion is estimated by tracing the edges of the spectrum, and the x-directional motion is canceled by shifting the spectrum in inverse direction. Next, the y-directional motion is canceled using a new constraint, with which the motion component and the true image component can be separated. The algorithm is shown to be effective by simulations.