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For the data stream characteristics of continuous, unbounded and real-time, continuous queries over data streams are generally based on windows. Windows placed on data streams are maintained by operators themselves for a query in most DSMSs. However, some operators can't maintain the windows properly, and a lot of redundancy and inconsistency may be incurred because the tuples are heavily copied and operators interfere with each other. In this paper, we thoroughly discuss the query processing mechanism based on windows and analyze the window semantics in a query sentence, then propose a query processing approach MullayerQuery that extract stream window and operator windows from the query window. A strategy and some algorithms are given to keep the consistency among windows in a query. The experiments show that MullayerQuery runs effectively and efficiently.