  K. Grove, L. Verdiani, B. Wilking and W. Ziller gave the first examples of
cohomogeneity one manifolds which do not carry invariant metrics with
non-negative sectional curvatures. In this paper we generalize their results to
a larger family. We also classified all class one representations for a pair
(G;H) with G/H some sphere, which are used to construct the examples.
