Introduces a new criterion for analytic rotation based upon the concept of simple structure. The rationale for the method stems from a consideration of the way in which the variance of squared factor loadings is partitioned as in an analysis of variance. It is argued that a maximization of the relative amount of squared factor loading variation which is due to the ‘interaction’ of factors and tests should produce results consistent with the simple structure hypothesis. Other methods of orthogonal rotation, such as quartimax and varimax, may be defined as linear combinations of the component sums of squares. The criterion of this paper differs from previous ones in that it is defined as a ratio of sums of squares. The use of a gradient method to maximize the criterion is discussed. A method for employing the Fletcher‐Powell algorithm is presented. The solutions obtained with three well‐known illustrative examples are similar to those obtained with varimax, although two of them are somewhat closer than varimax to Harman's subjective so