  We define left relative H-separable tower of rings and continue a study of
these begun by Sugano. It is proven that a progenerator extension has right
depth two if and only if the ring extension together with its right
endomorphism ring is a left relative H-separable tower. In particular, this
applies to twisted or ordinary Frobenius extensions with surjective Frobenius
homomorphism. For example, normality for Hopf subalgebras of finite-dimensional
Hopf algebras is also characterized in terms of this tower condition.
