Let N be an n-dimensional complete orientable Riemannian manifold isometrically immersed in an \((n+1)\)-dimensional model space (M,0). When the Gauss map on N based at the point 0 has constant rank, then N is foliated by special submanifolds. This result is due to \textit{J. L. Weiner} in the case where the model space is a space form [Proc. Am. Math. Soc. 38, 157-161 (1973; Zbl 0255.53033)].