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Let $D$ be a bounded domain in ${\mathbf{C}}^n$ such that the boundary $bD$ is topologically $S^{2n-1}$ in ${\mathbf{R}}^{2n}$ with a regular point; let $f:\tilde{D}\to {\mathbf{C}}^n$ be a holomorphic map where $\tilde{D}$ is a neighborhood of $\bar{D}$. If $f$ is one-to-one when restricted to $bD$, then $f:D\to f\left(D\right)$ is biholomorphic.