We discuss the structure of the Motzkin algebra [Formula: see text] by introducing a sequence of idempotents and the basic construction. We show that [Formula: see text] admits a factor trace if and only if [Formula: see text] and the higher commutants of these factors depend on [Formula: see text]. Then a family of irreducible bimodules over these factors is constructed. A tensor category with [Formula: see text] fusion rule is obtained from these bimodules.