A dispersion relation is set up for transverse waves in a plasma with an ellipsoidal velocity distribution. It is shown that the most unstable wave has its wavenormal parallel to the shortest axis of the ellipsoid and its vector potential parallel or anti-parallel to the longest axis. The maximum possible amplification rate is then calculated. Ellipsoidal velocity distributions arise in any flow with an anisotropic pressure tensor. If the resulting instability leads to a microscopic redistribution of particle velocities, then the effective transport coefficients of the plasma are changed. In Particular it is shown that the effective viscosity is decreased, and becomes dependent on the local gradient of the macroscopic velocity.