A modification of the quartimax computation for factor rotation is described in which a hypothesized factor pattern is given to the machine along with the data. The machine uses the pattern to select the subset of variables to which it will attend when rotating in a given plane, in order to find an orthogonal solution which closely fits the hypothesis. The program also provides a measure of the goodness of this fit. It can utilize pattern matrices that reflect only partial hypotheses as to the nature of the factors, as well as those that specify a determinate or over-determinate simple structure. Since the experimenter has a wide choice of patterns that he may wish to employ, he may expect to compute practically any solution he wants. At the same time, the nature of the constraints made on the results by the choice of pattern will be clearly evident.