We introduce a new Euclidean distance transformation (EDT) for binary images in Z(n), n greater than or equal to 3 by combining; our sufficient propagation EDT with the method of Saito and Toriwaki. Tests in Z(3) show that this new method is always faster than other well known EDTs and, especially, faster than the raster-scanning chamfer distance transformation. Moreover, we can efficiently implement it in parallel using a divide-and-conquer strategy.