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For 
$n\in \mathbb{Z}$ and 
$A\subseteq \mathbb{Z}$, define 
$r_{A}(n)$ and 
${\it\delta}_{A}(n)$ by 
$r_{A}(n)=\#\{(a_{1},a_{2})\in A^{2}:n=a_{1}+a_{2},a_{1}\leq a_{2}\}$ and 
${\it\delta}_{A}(n)=\#\{(a_{1},a_{2})\in A^{2}:n=a_{1}-a_{2}\}$. We call 
$A$ a unique representation bi-basis if 
$r_{A}(n)=1$ for all 
$n\in \mathbb{Z}$ and 
${\it\delta}_{A}(n)=1$ for all 
$n\in \mathbb{Z}\setminus \{0\}$. In this paper, we prove that there exists a unique representation bi-basis 
$A$ such that 
$\limsup _{x\rightarrow \infty }A(-x,x)/\sqrt{x}\geq 1/\sqrt{2}$.
