We present a new algorithm for optimally computing from point correspondences over two images their 3-D positions using the knowledge that they are constrained to be on a planar surface. We consider two cases: the case in which the plane and camera parameters are known and the case in which they are not. In the former, we show how observed point correspondences are optimally corrected so that they are compatible with the homography between the two images. In the latter, we show how the homography is optimally estimated by iteratively using the triangulation procedure. Although the accuracy improvement over existing methods is very small, our algorithm has a theoretical merit of computing an exact maximum likelihood solution.