AbstractThis paper addresses the problem of motion artifact cancellation in the standard 2D‐FFT MRI. Although motion is possible in any direction, in clinical MRI diagnosis, respiration is considered to be the main cause of motion. As a first order of approximation, motion due to respiration is assumed to be only in the phase‐encoding direction (Y‐axis) in this paper. In the previous approach, the region of a target object is assumed to be known and an iterative procedure is required. The problem of the algorithm is the convergence of the iterative (which may take a lot of time) and still has no guarantee of convergence. To avoid an iterative procedure, a new constraint is proposed here, with which the motion component and the true image component can be separated by a simple algebraic operation. After the Fourier transform of MRI signal along the read‐out direction (X‐direction), the phase of the spectrum alongY‐axis is expressed as an algebraic sum of the motion component and the true image component. On the other hand, when density distribution is symmetric along a Y‐direction line, such as a slice line on subcutaneous fat, the phase of the Fourier spectrum along the line is a linear function ofY‐position. Therefore, if the density is symmetric, the departure from the linear function of the phase is just the motion component. With this constraint the motion component can be estimated and the motion artifact in MRI can be canceled. The algorithm is shown to be effective using a phantom with simulated motions in various cases. When the density distribution along theY‐directional line on subcutaneous fat is not perfectly symmetric, the accuracy of estimated motion will be affected to some extent. However, this method is shown to be still effective in such general ca