Let $q^{n}$ be the KT coding distribution on $\mathcal{X}^{n}$, where $|\mathcal{X}|=m$. Then for any pmf $p(x)$ on $\mathcal{X}$ and iid source distribution $p^{n}(x^{n})=\prod_{i=1}^{n}p(x_{i})$ $$\frac{1}{n}D(p^{n}\|q^{n})\le \frac{m-1\log n}{2n}+\frac{K_{0}}{n}, \ \ \forall n\ge1$$for some constant $K_{0}$.