In this article, the concept of constraint factor is proposed, and a new hysteretic operator consisting of a constraint factor and a polynomial is presented. Based on the constructed hysteretic operator, the one-to-multiple mapping of hysteresis is transformed into one-to-one mapping by expanding the input space, so that the mapping between the expanded input space and the output space comprises one-to-one and multiple-to-one mappings. Finally, a neural network is employed to approximate hysteresis for piezoelectric actuators. The validation performance of experimental tests suggests that the proposed approach is effective.