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[en] The in situ logic operation on memristor memory has attracted researchers' attention. In this brief, a new circuit structure that performs a stateful OR logic operation is proposed. When our OR logic is operated in series with other logic operations (IMP, AND), only two voltages should to be changed while three voltages are necessary in the previous one-step OR logic operation. In addition, this circuit structure can be extended to multi-inputs OR operation to perfect the family of logic operations on memristive memory in nanocrossbar based networks. The proposed OR gate can enable fast logic operation, reduce the number of required memristors and the sequential steps. Through analysis and simulation, the feasibility of OR operation is demonstrated and the appropriate parameters are obtained.