A topological space is reversible if every continuous bijection f:X→X is a homeomorphism. There are many examples of reversiblespaces; in particular, Hausdorff compact spaces and locally Euclidean spaces are such. Chatyrko and Hattori observed, in a manuscript, that any product of topological spaces is non-reversible whenever at least one of the spaces is non-reversible and asked whether the topological product of two connected reversible spaces is reversible. The authors prove here that there are connected reversible spaces such that their product is not reversible. In fact, they construct a reversible space X which is a connected 2-manifold in R3 without boundary such that X×[0,1] is not reversible.