  In this note, We proved that a compact Sasakian manifold $( M, {\xi}, {\eta},
{\Phi} , g )$ with negative transverse holomorphic sectional curvature must
have has a Sasakian structure $( {\xi}, {\eta} , {\Phi} , g )$ with negative
transverse Ricci curvature. Similarly, a compact Sasakian manifold with
non-positive transverse holomorphic sectional curvature, then the negative
first basic Chern class is transverse nef and we have the Miyaoka-Yau type
inequality. When transverse holomorphic sectional curvature is quasi-negative,
we obtain a Chern number inequality.
