  We give an example of a domain in dimension $N \geq 3$, homeomorphic to a
ball and with analytic boundary, for which the second eigenvalue of the
Dirichlet Laplacian has an eigenfunction with a closed nodal surface. The
domain is constructed via a sequence of perturbations of the domain of S.
Fournais [J. Differential Equations \textbf{173} (2001), 145-159].
