  We consider the two permutation statistics which count the distinct pairs
obtained from the last two terms of occurrences of patterns t_1...t_{m-2}m(m-1)
and t_1...t_{m-2}(m-1)m in a permutation, respectively. By a simple involution
in terms of permutation diagrams we will prove their equidistribution over the
symmetric group. As special case we derive a one-to-one correspondence between
permutations which avoid each of the patterns t_1...t_{m-2}m(m-1) in S_m and
such ones which avoid each of the patterns t_1...t_{m-2}(m-1)m. For m=3, this
correspondence coincides with the bijection given by Simion and Schmidt in
their famous paper on restricted permutations.
