An ingenious simple trick enables the author to improve a previous result of myself, Z. Galil, and O. Margalit [1] for an interesting special case. He obtains an algorithm that finds the distances between all pairs of vertices of an n -vertex undirected and unweighted graph in time O ( M ( n ) log n ), where M ( n ) is the time needed to multiply two n -by- n matrices of small integers (which is known to be O ( n ^2.376 ). This is a beautiful short note. A more general (but more complicated) algorithm that works for the case of small weights as well has been found by Galil and Margalit.