In three-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>=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 one-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.