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It is known that a graph $G$ is bipartite if and only if there is an orientation $\\sigma$ of $G$ such that $Sp_S(G^\\sigma)=iSp(G)$. In [D. Cui, Y. Hou, On the skew spectra of Cartesian products of graphs, Electron. J. Combin. 20(2013), #P19], Cui and Hou conjectured that such orientation of a bipartite graph is unique under switching-equivalence. 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