The product Gi□G2 is the graph with the cartesian product V(G1)×V(G2) as its vertex set

in which the vertex (u

v) is adjacent to (x

y) if and only if either u = x and v is adjacentto y in G2 or v = y and u is adjacent to x in G1. We show that for every spanning tree T of graph Cm□Cn with m and n not both even

there exists an edge of graph Cm□Cn outside T whose addition to T forms a cycle of length at least m+n-1 . This solves an open problem posed by Chen(Discrete Mathematics 287(2004) 11-15).