A scaling technique known as the Method of Reciprocal Averages has been in use since the early 1930's. This technique yields a set of item response weights for a psychological inventory which maximizes the internal consistency of the inventory for a group of subjects. Although the technique has been used for many years, its mathematical foundations have not been made explicit. In the present paper, it is shown that the informal data processing procedures of this technique actually solve the set of linear equations yielded by Guttman's Least Squares Model for internal consistency scaling. The Method of Reciprocal Averages can be implemented as a simple extension to existing item analysis computer programs. (Author/CK)