The performance of a number of image processing methods depends on the output quality of a distance transformation (DT) process. Most of the fast DT methodologies are not accurate, whereas other error-free DT algorithms are not very fast. In this paper, a novel, fast, simple, and error-free DT algorithm is presented. By recording the relative $x$- and $y$-coordinates of the examined image pixels, an optimal algorithm can be developed to achieve the DT of an image correctly and efficiently in constant time without any iteration. Furthermore, the proposed method is general since it can be used by any kind of distance function, leading to accurate image DTs.