  In this paper, a (3\times3)-matrix representation of the
Birman-Wenzl-Murakami(BWM) algebra has been presented. Based on which, unitary
matrices (A(\theta,\phi_1,\phi_2), B(\theta,\phi_1,\phi_2)) are generated via
the Yang-Baxterization approach. A hamiltonian is constructed from the unitary
(B(\theta,\phi)) matrix. We then study the Berry phase of the Yang-Baxter
system and find the topological parameter d has relationship with berry phase.
