A "doubly-centered" raw data matrix is one for which both columns and rows have both unit variance and means equal to zero. The factor scores from one analysis are the same as factor pattern coefficients from the other analysis except for a variance adjustment. This study explored an extension of the reciprocity principle which may have applications in some research situations. Analysis of an actual data set was used to illustrate the technique. The Multiple Teachers Factor Survey measured perceptions of four "teacher-types" by undergraduate students. A procedure was presented for calculating factor scores when subjects have rated several referents or the researcher wishes to compare factor scores for different subject groups. The procedure was the application of a conventional factor score coefficient matrix to a doubly-centered matrix of standardized scores. Tables illustrate two-mode techniques, a doubly-centered data matrix, varimax rotated pattern coefficients, cosines among factor axes, means and confidence intervals, and first subject's factor scores. (DWH)