In this study, an improved post-processing technique for correcting MRI artifact due to the unknown respiratory motion in the imaging plane is presented. Respiratory motion is modeled by a two-Dimensional linear expending-shrinking movement. Assuming that the body tissues are incompressible fluid like materials, the proton density per unit volume of the imaging object is kept constant. According to the introduced model, respiratory motion imposes phase error, non-uniform sampling and amplitude modulation distortions on the acquired MRI data. When the motion parameters are known or can be estimatead a reconstruction algorithm based on biliner superposition method was used to correct the MRI artifact. In the case of motion parameters are unknown, first, the spectrum shift method is applied to find the respiratory fluctuation function, x directional expansion coefficient and x directional expansion center. Next, y directional expansion coefficient and y directional expansion center are estimated by using the minimum energy method. Finally, the validity of this proposed method is shown to be effective by using the simulated motion images.