  We prove some structure results for \emph{transverse reducible} Sasaki
manifolds. In particular, we show Sasaki manifolds with positive Ricci
curvature is transversely irreducible, and so there is no join (product)
construction for irregular Sasaki-Einstein manifolds, as opposed to the
quasi-regular case done by Wang-Ziller and Boyer-Galicki. As an application, we
classify compact Sasaki manifolds with non-negative transverse bisectional
curvature, which can be viewed as the generalized Frankel conjecture (N. Mok's
theorem) in Sasaki geometry.
