This paper gives a new method for the rectification. The method is based on an examination of the fundamental matrix, which describes the epipolar geometry of the image pair. The approach avoids camera calibration and makes the resampling images extremely simple by using Bresenham Algorithm to extract pixels along the corresponding epipolar line. For a large set of camera motions, remapping to a plane has the drawback of creating rectified images that are potentially infinitely large and presents a loss of pixel information along epipolar lines. In contrast, our method guarantees that the rectified images are bounded for all possible camera motions and minimizes the loss of pixel information along epipolar lines. Furthermore, it never splits the image so that connected regions are no longer connected even if the epipole locates in the image. A large number of intensive experiments have been carried out, and the results show that more accurate matches can be obtained for initial pair of images after the rectification.