will mainly work with a [*normal*]{} $(n-1)$-complete $X$, and we recall that a reduced complex space $\big(X, \mathcal{ O}_X \big)$ is [*normal*]{} if the sheaf of [*weakly holomorphic functions*]{}, namely functions defined and holomorphic on the regular part $X_{\rm 
reg} = X \backslash X_{\rm
sing}$ which are $L_{\rm loc}^\infty$ on $X$, coincides with the complete sheaf $\mathcal{ O}_X$ of holomorphic functions on $X$. Then $X_{\rm
sing}$ is of codimension $\geqslant 2$ at every point of $X$ ([@fi1976; @gu1990]) and for every open set $U \subset X$, both restriction maps $$\mathcal{O}_X(U)
\longrightarrow
\mathcal{O}_X\big(
U\backslash X_{\rm sing}
\big)
\ \ \ \ \ 
\text{\rm and}
\ \ \ \ \ 
\mathcal{M}_X(U)
\longrightarrow
\mathcal{M}_X\big(
U\backslash X_{\rm sing}
\big)$$ are bijective[^3], where $\mathcal{ M }_X$ denotes the meromorphic sheaf. To generalize Hartogs extension, normality of $X$ is an unavoidable assumption, because there are examples of Stein surfaces $S$ having a single singular point $\widehat{ p}$ which are [*not*]{} normal ([@gu1990], vol. II, p. 196), whence $K := \{ \widehat{ p} \}$ fails to be removable for holomorphic functions defined in a neighborhood of $K$.

We can now state our main result.

Let $X$ be a connected $(n-1)$-complete normal complex space of pure dimension $n\geqslant 