  Let $Z^{\alpha,\beta}$ be the Rosenblatt sheet with the representation $$
Z^{\alpha,\beta}(t,s)=\int^t_0\int^s_0\int^t_0\int^s_0Q^\alpha(t,y_1,y_2)Q^\beta(s,u_1,u_2)B(dy_1,du_1)B(dy_2,du_2)
$$ where $B$ is a Brownian sheet, $\frac12<\alpha,\beta<1$, $Q^\alpha$ and
$Q^\beta$ are the given kernel. In this paper, we contruct multiple Wiener
integrals of the form \begin{align*}
\int^t_0\int^s_0\int^t_0\int^s_0&[k_1(y_1,y_2)^{-\frac12\alpha}(u_1,u_2)^{-\frac12\beta}+k_2(y_1\vee
y_2)^{\frac12\alpha}(y_1\wedge y_2)^{-\frac12\alpha}|y_1-y_2|^{\alpha-1}\\
&\cdot(u_1\vee u_2)^{\frac12\beta}(u_1\wedge
u_2)^{-\frac12\beta}|u_1-u_2|^{\beta-1}]B(dy_1,du_1)B(dy_2,du_2),~~k_1,k_2\geq0,
\end{align*} and obtain an optimal approximation of $Z^{\alpha,\beta}(t,s)$.
