  In 3-dimensional Euclidean space, Scherk second surfaces are singly periodic
embedded minimal surfaces with four planar ends. In this paper, we obtain a
natural generalization of these minimal surfaces in any higher dimensional
Euclidean space ${\R}^{n+1}$, for $n \geq 3$. More precisely, we show that
there exist $(n-1)$-periodic embedded minimal hypersurfaces with four
hyperplanar ends. The moduli space of these hypersurfaces forms a 1-dimensional
fibration over the moduli space of flat tori in ${\R}^{n-1}$. A partial
description of the boundary of this moduli space is also given.
