Write p 1, p 2…p m for the permutation matrix δ pi, j . Let S n (M) be the set of n×n permutation matrices which do not contain the m×m permutation matrix M as a submatrix. In [7] Simion and Schmidt show bijectively that |S n (123) |=|S n (213) |. In [9] this was generalised to a bijection between S n (12 p 3…p m ) and S n (21 p 3…p m ). In the present paper we obtain a bijection between S n (123 p 4…p m ) and S n (321 p 4…p m ).