Ishihara and Obata2 have proved that if M is a differentiable and connected Riemannian manifold of dimension > 2, which is not locally Euclidean and if M admits a conformal transformation such that the associated function ( satisfies ( (x) < 1 ε, or ((x) > 1+ε, for each x M, being a positive number, then has no fixed point. Further, Hirmatu1 has studied that a differentiable and connected Riemannian manifold admitting a conformal transformation group of sufficiently high dimension is locally conformal Euclidean. In the present paper, we have obtained results concerning the fixed point of a conformal transformation of a Kaehlerian space and concerning the locally conformally flatness of the Kaehlerian space.