Electromagnetic instabilities associated with transverse plasma waves propagating perpendicular to an external uniform magnetic inductionB0are investigated for a two‐temperature Maxwellian distribution function. The analysis shows that no instability develops ifV‖e2< V⊥e2whereV‖e2andV⊥e2are the electron temperatures parallel and perpendicular toB0. ForV‖e2> V⊥e2an instability develops if&ohgr;ce2/&ohgr;pe2< V‖e2/c2[1 − (32)12(V⊥e/V‖e)]where&ohgr;ceand&ohgr;peare the cyclotron and plasma frequency, respectively, andcis the velocity of light. The allowable frequency regions for this type of electromagnetic wave to exist acrossB0are studied. It is found that below the plasma frequency there is always a narrow allowable frequency band just below any harmonics of the ion or electron cyclotron frequencies. Each width of the allowable frequency band is calculated.