The general dispersion formulas of plasma waves propagating perpendicular to an applied uniform magnetic fieldB0in an infinite plasma are derived. Stability of one of the wave modes, a linearly polarized electromagnetic wave whose electric field is directed alongB0, is analyzed under the assumption that the wavelength is much larger than the cyclotron radii of electrons. The analysis shows that the waves are stable for a low‐density plasma. However, if the plasma density becomes sufficiently high such that the plasma frequency becomes higher than the electron cyclotron frequency, then an instability may develop. The stability criterion is compared with and is analogous to the criterion for the firehose instability. the allowable frequency range for this mode is analyzed, and it indicates that there is no longer a low‐frequency cutoff in the rigorous sense for a hot plasma.