The usual method of carrying out a higher‐order factor analysis is simply to factor the matrix of intercorrelations between the factors of a lower level. It has been found difficult to achieve good simple structure when these higher‐order factors are rotated by means of an analytic rotation procedure. Instead, it is proposed that the projections of the original variables on an orthogonal higher‐order matrix should be computed and that this matrix should be rotated rather than the higher‐order factor matrix. Comparisons have been made between the old method and this new method for the same sets of data. The new method was thought to be superior in several r