A singular Riemannian foliation is a subdivision of a Riemannian manifold into submanifolds (leafs) of possible different dimension such that the leafs are locally equidistant. One can try to associate to such a foliation a new foliation by defining the leaf of a point p as the set of all points that can be joined with p by a horizontal path. The main result asserts that in the presence of nonnegative sectional curvature on the ambient manifold this defines again a Riemannian foliation.