Abstract. The paper is devoted to the question of orienting the edges of a graph to obtain a digraph with the maximum possible Wiener index. (Here, if there is not a directed u-v path in the digraph, then the ordered pair contributes 0 to the Wiener index.) In a previous paper it was proved that in the 2xn grid the maximum Wiener index is obtained when all edges in factors are directed paths which are directed in the same way except the one corresponding to a pendant vertex, which is directed in the opposite way. And it was conjectured that the same holds for mxn grids if m\ge 3. We disprove the conjecture by showing that a comb-like orientation achieves significiantly bigger Wiener index.