  In this paper, we propose a notion of colored Motzkin paths and establish a
bijection between the $n$-cell standard Young tableaux (SYT) of bounded height
and the colored Motzkin paths of length $n$. This result not only gives a
lattice path interpretation of the standard Young tableaux but also reveals an
unexpected intrinsic relation between the set of SYTs with at most $2d+1$ rows
and the set of SYTs with at most 2d rows.
