Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let ${mu}0$ be the least eigenvalue of the Laplacian acting on $L^2-functions$ on M. We show that if $Ric^M{ge}-{mu}0$ at all $x{in}M$ and either $Ric^M>-{mu}0$ at some point x0 or Vol(M) is infinite, then every harmonic morphism ${phi}:M{ o}N$ of finite energy is constant.