An extension theorem for normal functions

Given a domain $\Omega \subset {{\mathbf{C}}^n}$, an analytic subvariety $V$ of $\Omega$ and a normal function $f:\Omega \backslash V \to \widehat{\mathbf{C}}$, we show that $f$ can be extended to a holomorphic mapping ${f^*}:\Omega \to \widehat{\mathbf{C}}$ provided the singularities of $V$ are normal crossings.