AbstractLet f(n) be the minimum number of colors required to color the edges of Kn,n such that every copy of K3,3 receives at least three colors on its edges. We prove that $$(0.62+o(1))\sqrt{n}< \, f(n)< \, (1+o(1))\sqrt{n}$$, where the upper bound is obtained by an explicit edge‐coloring. This complements earlier results of Axenovich, Füredi, and Mubayi [1]. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 193–198, 2003