  Let $n\ge 2$ be an integer, and $B^{n}\subset \mathbb{C}^{n}$ the unit ball.
Let $K\subset B^{n}$ be a compact subset such that $B^n\setminus K$ is
connected, or $K=\{z=(z_1,\cdots, z_n)|z_1=z_2=0\}\subset \mathbb{C}^{n}$. By
the theory of developing maps, we prove that a K\"{a}hler metric on
$B^{n}\setminus K$ with constant holomorphic sectional curvature uniquely
extends to $B^{n}$.
