Let $(R,m)$ be a $d$-dimensional regular local ring with quotient field $K$ and $(S,n)$ be a $d$-dimensional normal local domain birationally dominating $R$ with $l(mS) = d$. In this paper, it is shown that the following three properties hold.

1. $S$ is dominated by the $m$-adic prime divisor of $R$;

2. $n^i \cap R = m^i$, for all $i \ge 1$;

3. $R/m = S/n$.