  Baryshnikov and Romik derived the combinatorial identities for the numbers of
the $m$-strip tableaux. This generalized the classical Andr\'e's theorem for
the number of up-down permutations. They asked for a bijective proof for the
enumeration of $3$-strip tableaux. In this paper we will provide such a
bijective proof. First we count the $3$-strip tableaux by decomposition.
Secondly we will apply this "decomposition" idea on the up-down permutations
and down-up permutations to enumerate the $3$-strip tableaux bijectively.
