Due to the continuous growth of wireless communication technology and mobile equipment, the history management of moving object is important in a wide range of location-based applications. To process queries for history data, trajectories, we generally use trajectory-preserving index schemes based on the trajectory preservation property. This property means that a leaf node only contains segments belonging to a particular trajectory, regardless of the spatiotemporal locality of segments. The sacrifice of spatiotemporal locality, however, causes the index to increase the dead space of MBBs of non-leaf nodes and the overlap between the MBBs of nodes. Therefore, an index scheme for trajectories shows good performance with trajectory-based queries, but not with coordinate-based queries, such as range queries. We propose new index schemes that improve the performance of range queries without reducing performance with trajectory based queries.