  Classifying the nonflat hypersurfaces in Euclidean space $f\colon
M^n\to\mathbb{R}^{n+1}$ that locally admit smooth infinitesimal deformations
that preserve the Gauss map infinitesimally was a problem only considered by
Schouten \cite{Sc} in 1928. He found two conditions that are necessary and
sufficient, with the first one being the minimality of the submanifold. The
second is a technical condition that does not clarify much about the geometric
nature of the hypersurface. In that respect, the parametric solution of the
problem given in this note yields that the submanifold has to be Kaehler.
