Direction relations deal with order in space. Recently, direction relation query processing has gradually gained attention in geospatial databases applications, such as Spatial Data Mining (SDM) and GIS (geographic information system). The processing of direction relation queries needs spatial join operations. Until now, the research work on processing of spatial joins has primarily focused on topological and distance relations. There is little work on processing joins with direction predicates. This paper presents an efficient method for processing direction relation queries using R-trees. The quad-tuples model is defined to represent direction relations between MBRs (minimum bounding rectangles) of spatial objects. An algorithm of processing the filter step using R-trees is given and the refinement step is further decomposed into three different operations. The method presented can efficiently process direction relation queries between objects of any data types in a 2D space. Using both direction and distance constraints restricting the search space when traversing R-trees, this paper also presents an algorithm of direction relation query processing in SDM. Performance evaluation of the proposed method is conducted using real world datasets and the experiment results show that it performs well with respect to both I/O- and CPU-time.