  Let $D$ be a non-pseudoconvex open set in $\C^3$ and $S$ be the union of all
two-dimensional planes with non-empty and non-pseudoconvex intersection with
$D.$ Sufficient conditions are given for $\C^3\setminus S$ to belong to a
complex line. Moreover, in the $\mathcal C^2$-smooth case, it is shown that
$S=\C^n$.
