Suppose two maps $f_{0}:\hat{A}(1,100)\rightarrow B(q,200)$, $f_{1}:\hat{A}(1-\delta,100+\delta)\rightarrow B(q,200)$ satisfy that for $i=0,1$ and some $r>0$, $(1-\epsilon)|x|\leq 10^{i}r^{-1}d(q,f_{i}(x))\leq(1+\epsilon)|x|,$ and $|10^{2i}r^{-2}f_{i}^{*}g-g_{0}|_{C^{4}}\leq\epsilon$ on $\hat{A}(10^{i},10^{i+1})$. Then there is a constant $G=G(\epsilon)$ with $\lim_{\epsilon\rightarrow 0}G(\epsilon)=0$, a rotation $R\in O(4)$, and a map $f:\hat{A}(10^{-1},100)\rightarrow B(q,200)$, with $f(x)=f_{0}(x)$ on $\hat{A}(9,100)$, $f(x)=f_{1}(10R^{-1}(x))$ on $\hat{A}(10^{-1},2)$, and $|r^{-2}f^{*}g-g_{0}|_{C^{2}}\leq C(\epsilon)$ on $\hat{A}(10^{-1},100)$.