  Given a smooth compact hypersurface $M$ with boundary $\Sigma=\partial M$, we
prove the existence of a sequence $M_j$ of hypersurfaces with the same boundary
as $M$, such that each Steklov eigenvalue $\sigma_k(M_j)$ tends to zero as $j$
tends to infinity. The hypersurfaces $M_j$ are obtained from $M$ by a local
perturbation near a point of its boundary. Their volumes and diameters are
arbitrarily close to those of $M$, while the principal curvatures of the
boundary remain unchanged.
