In order to investigate the non-odd-bipartiteness of even uniform hypergraphs, we introduce a class of k-uniform hypergraphs G, called (k, k/2)-hypergraphs, which satisfy the property: k is even, every edge e of G can be divided into two disjoint 2k--vertex sets say e1 and e2 and for any edge e incident to e, e ∩ e =e1 or e2.Such graph G can be constructed from a simple graph, which is called the underlying graph of G.We show that G is non-odd-bipartite if and only if the underlying graph of G is non-bipartite.