  A method of constructing Temperley-Lieb algebras(TLA) representations has
been introduced in [Xue \emph{et.al} arXiv:0903.3711]. Using this method, we
can obtain another series of $n^{2}\times n^{2}$ matrices $U$ which satisfy the
TLA with the single loop $d=\sqrt{n}$. Specifically, we present a $9\times9$
matrix $U$ with $d=\sqrt{3}$. Via Yang-Baxterization approach, we obtain a
unitary $ \breve{R}(\theta ,\varphi_{1},\varphi_{2})$-matrix, a solution of the
Yang-Baxter Equation. This $9\times9$ Yang-Baxter matrix is universal for
quantum computing.
