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From the result that a bipartite graph $G$ admits an orientation $G^e$ such that every cycle is oddly oriented if and only if it contains no even subdivision of $K_{2,3}$, Yan and Zhang showed that the permanental polynomial of such a bipartite graph $G$ can be expressed as the characteristic polynomial of the skew adjacency matrix $A(G^e)$. In this paper we first prove that this equality holds only if the bipartite graph $G$ contains no even subdivision of $K_{2,3}$. 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