  In this paper, we show that every harmonic map from a compact K\"ahler
manifold with uniformly RC-positive curvature to a Riemannian manifold with
non-positive complex sectional curvature is constant. In particular, there is
no non-constant harmonic map from a compact K\"ahler manifold with positive
holomorphic sectional curvature to a Riemannian manifold with non-positive
complex sectional curvature.
