The interaction sum of squares with (n−1)2 D.F. from a replicated n×n factorial experiment is partitional into two independently distributed components, the relatedness s.s. and the symmetrical difference s.s. The two s.s. are based on rij = c^ij +c^ji− c^ii −c^jj and S^ij = c^ij − c^ji respectively, i, j = 1, 2,…, n, where c^ij is the least squares estimate of the i, jth cell interaction. The relatedness s.s. is subdivided into three independently distributed sums of squares with 1, n−1 and I/2n(n−3) D.F. respectively and the symmetrical difference s.s. into two independent sums of squares with n−2 and 〈n−22〉 D.F. respectively.