  Let $D, G\subset{\Bbb C}$ be domains, let $A\subset D$, $B\subset G$ be
locally regular sets, and let $X:=(D\times B)\cup(A\times G)$. Assume that $A$
is a Borel set. Let $M$ be a proper analytic subset of an open neighborhood of
$X$. Then there exists a pure 1-dimensional analytic subset $\hat M$ of the
envelope of holomorphy $\hat X$ of $X$ such that any function separately
holomorphic on $X\setminus M$ extends to a holomorphic function on $\hat
X\setminus\hat M$. The result generalizes special cases which were studied in
\cite{\"Okt 1998}, \cite{\"Okt 1999a}, and \cite{Sic 2000}.
