A gyrotropic plasma withT∥/T⊥≡ &ggr; < 1, whereT⊥andT∥are the transverse and longitudinal temperatures, is shown to be unstable to a perturbation in the form of a transverse wave with a wave vectorksuch thatk2<k02= {&ohgr;c2(1−&ggr;)2+ &ohgr;p2(1−&ggr;)/&ggr;}/c2, &ohgr;cand &ohgr;pare the gyro and plasma frequencies. ForT∥>T⊥such an instability arises only if &ohgr;c2/&ohgr;p2> 1/&ggr;(&ggr;−1) and then only fork2<k02. However, in the latter case, the phase velocity of the instability exceedscand the growth rate must be made to vanish because of relativistic considerations. No such instability arises for complete isotropyT⊥=T∥.