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Dedicated to Professor L. K. Hua, who was the teacher of Professor J. Q. Zhong. Zhong was the teacher of Guan in China and led him into this topic. Guan still have copies of papers of Calabi and Futaki which Zhong showed him in 1986.

In this note we prove a splitting theorem for compact complex homogeneous spaces with a cohomology 2 class [w] such that the top power [wn] # 0. Mathematics Subject Classifications (1991): 53C15, 57T15,53C30, 53C56', 53C50.