In 1985, Rodica Simion and Frank Schmidt gave a bijection between
the permutations avoiding the subsequence 123 and those avoiding 213.
In other words they showed that S_n(123) <-> S_n(213). This was
extended by West to S_n(12p_3...p_m) <-> S_n(21p_3...p_m) and then
by West and Babson to S_n(123p_4...p_m) <-> S_n(321p_r...p_m).
In this paper we give the final extension, to
S_n(12...tp_{t+1}...p_m) <-> S_n(t...21p_{t+1}...p_m). Moreover
we show that the same bijection applies to transversals of any
Young diagram, not just a square shape.