Let \(M^ n\subset R^{n+1}\) be a complete orientable minimal hypersurface in the Euclidean space \(R^{n+1}\). For \(n=2\), it is known that if \(M^ 2\) is stable then it is a plane. The existence of nontrivial minimal graphs for \(n\geq7\) shows that there exist stable hypersurfaces that are homeomorphic to \(R^ n\) but are not hyperplanes. In this interesting paper, the author describes a simple topological obstruction to stability for arbitrary \(n\); namely, if \(M^ n\) contains a codimension one cycle which does not separate \(M^ n\), then \(M^ n\) is unstable.