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Most results on the polynomial-like iterative equation are given under the con-dition that the given function is monotone,while a work by L.Liu and X.Gong gets non-monotone PM solutions with height 1 when the given function is of the same case.Removing the condition on height for the given function,we first give a method to assert the nonex-istence of C0 solutions,then present equivalent conditions for the existence of PM solutions with finite height.Finally,as an application of the equivalent conditions,we construct the PM solutions in the case that the given function has one fort.