RFID events are a large volume of stream data that continuously come out for tracking and monitoring objects. Many studies have been done to detect a complex event in the RFID stream. However, the existing studies have many problems which increase unnecessary operations when complex events do not satisfy minimum conditions. In this paper, we propose a new scheme to detect complex events when the minimum conditions are satisfied to remove unnecessary operations. To check the minimum conditions of the complex events, we register complex queries in a query index. We detect complex events using the query index and bitmap. To demonstrate the superiority of the proposed method, we compare it with the existing methods through various experiments. As a result, it is shown that the proposed method outperforms the existing methods as a whole.