Range query is one of the most important operations for spatial objects, it retrieves all spatial objects that overlap a given query region in multi-dimensional space. The DOT(DOuble Transformation) is known as an efficient indexing methods, it transforms the MBR of a spatial object into a single numeric value using a space filling curve, and stores the value in a $B^+$-tree. The DOT index is possible to be employed as a primary index for spatial objects. However, the range query processing based on the DOT index requires much overhead for spatial transformations to get the query region in the final space. Also, the detailed range query processing method for 2-dimensional spatial objects has not been studied yet in this paper, we propose an efficient multi-dimensional range query processing technique based on the DOT index. The proposed technique exploits the regularities in the moving patterns of space filling curves to divide a query region into a set of maximal sub-legions within which space filling curves traverse without interruption. Such division reduces the number of spatial transformations required to perform the range query and thus improves the performance of range query processing. A visual simulator is developed to show the evaluation method and the performance of our technique.