Numerous methods have been proposed recently to analyze the spatial pattern of locations of earthquakes to infer planes along which earthquakes cluster. These planes are considered to be earthquake slip planes. The application of such methods is to find major planes passing through a set of earthquake locations when the fault plane solutions of the events are unusual or when locating planes would contribute to understanding the structural setting in which an earthquake occurred. A modification to one of these methods, the three-point method, allows one to study anomalous or otherwise interesting events, and to choose which nodal plane in the fault plane solution for the event is the plane of slip. To be successful, the method requires that a sufficient number of other events had the same, or similar, slip plane. The modified three-point method consists of finding the orientations of planes formed by combinations of the location of the earthquake under study and all other locations in the remainder of the earthquake catalog taken two at a time. A test to determine which orientations occur more often than expected is used to identify statistically significant planes along which earthquakes cluster. Each plane identified passes through the earthquake being studied. If one of these planes is parallel, or nearly parallel, to one of the nodal planes of the fault plane solution, that nodal plane is assumed to be the slip plane. The method is demonstrated by investigating ten earthquakes that occurred during 1983-1984 near Coalinga, California. Using the method, significant alignments of events along planes that are nearly parallel to one of the nodal planes for eight of the ten events were found. ¿ American Geophysical Union 1990