This work addresses the problem of detecting boundary points in data sets. Boundary points are data points that distribute the edge of densely distributed data such as the cluster. It describes a novel approach called FRINGE (an eFficient boundaRy poInts detectioN based on Grid and anglE) to detect boundary points. FRINGE employs the grid technique and the angle feature. Experimental studies on data sets with varying characteristics indicate that FRINGE is able to detect boundary points in the noisy dataset containing different shapes and sizes clusters effectively and has higher efficiency.