A class of algebras $D(m,d,\xi )$ introduced by ^[22] were not pointed and generated by the coradical of $D(m,d,\xi )$. Let $D$ be the quotient of $D(m,d,\xi )$ module the principle ideal $(g^m-1)$. First, we describe all simple left modules of $D$. Then, according to Radford's method, we construct the Yetter-Drinfeld module over $D$ by the tensor product of a simple module of $D$ and $D$ itself. Hence, we find some simple left Yetter-Drinfeld modules over $D$, and the relevant braidings are of a triangular type.