Let $\xi =[a_0;a_1,a_2,\cdots ,a_i,\cdots ]$ be an irrational number in simple continued fraction expansion, $p_i/q_i=[a_0;a_1,a_2,\cdots ,a_i]$, $M_i=q_i^2|\xi -p_i/q_i|$. In this note we find a function $G(R,r)$ such that $$\begin{array}{ccc}& M_{n+1}<R\text{and}{M}_{n-1}<r\text{imply}{M}_n>G(R,r),\hfill & \hfill M_{n+1}>R\text{and}{M}_{n-1}>r\text{imply}{M}_n<G(R,r).\end{array}$$ Together with a result the author obtained, this shows that to find two best approximation functions $\tilde{H}(R,r)$ and $\tilde{L}(R,r)$ is a well-posed problem. This problem has not been solved yet.