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This work addresses the problem of finding boundary points in multidimensional data sets. Boundary points are data points that are located at the margin of densely distributed data such as a cluster. We describe a novel approach called BORDER (a BOundaRy points DEtectoR) to detect such points. BORDER employs the state-of-the-art database technique - the Gorder kNN join and makes use of the special property of the reverse k nearest neighbor (RkNN). Experimental studies on data sets with varying characteristics indicate that BORDER is able to detect the boundary points effectively and efficiently.