The authors present an improvement to a sigma‐filter extrapolation method for the reconstruction of magnetic resonance (MR) images from symmetric discrete Fourier data. By making use of the phase information in the image data, the proposed method can overcome the data inconsistency problem of the original method for handling MR image data with large phase variations, such as those obtained in gradientecho pulse sequences. Reconstruction results show that its performance is comparable with that of the modified complex sigma‐filter method proposed previously to handle the inconsistency problem. However, the new approach has the advantage of reducing computation time by a factor of two with use of a sigma filter applied to real instead of complex images. It is expected that this method will be more practical for use in clinical MR imaging systems.