This paper describes a new method which is used in the process of determining composite focal mechanism solutions to objectively sort earthquakes into sets in which the P-wave first-motion data are compatible. For a network of n stations, each one of which can record either of two first motions (dilatation or compression), there are 2n mathematically possible patterns of first motions; only a few of these mathematically possible patterns are physically possible for a double-couple source. A comparison is made between the observed first-motion data from a set of earthquakes in a small source region to each of the 2n mathematically possible patterns. The comparison results in two parameters being assigned to each of the patterns: (1) the number of earthquakes which have first motions compatible with the pattern; and (2) the number of actual first-motion data for those earthquakes. Generally, one finds only a few patterns with high parameter values, and which are based on data from independent subsets of earthquakes. In all the cases examined so far, these few patterns are physically possible; i.e., they are compatible with double-couple focal mechanism solutions. The focal mechanism solution determined from a selected pattern of first motion is a composite solution because it is based on the first-motion data from a number of earthquakes.