Let $\{(M_{k},g_{k},J_{k},\omega_{k},p_{k})\}$ be a family of pointed compact Kähler n-manifolds with sectional curvature and injectivity radius at $p_{k}$

$$|K_{g_{k}}|\leq 1,\ \ \ i_{g_{k}}(p_{k})\geq C,$$

for a constant $C>0$ independent of $k$. Then a subsequence of $\{(M_{k},g_{k},J_{k},\omega_{k},p_{k})\}$ converges to a complete Kähler n-manifold $(X,g,J,\omega,p)$ in the pointed $C^{1,\alpha}$-sense, i.e. for any $r>0$, there are embeddings $F_{k,r}:B_{g}(p,r)\longrightarrow M_{k}$ such that $F_{k,r}(p)=p_{k}$, $F_{k,r}^{*}g_{k}$ (resp. $dF_{k,r}^{-1}J_{k}dF_{k,r}$ and $F_{k,r}^{*}\omega_{k}$) converges to $g$ (resp. $J$ and $\omega$) in the $C^{1,\alpha}$-sense.