Expressions for the propagation of a circularly polarized microwave through a plasma parallel to a uniform and static magnetic field are derived from the Boltzmann equation and, alternately, from the equation of motion of an individual electron. Both methods yield identically the same formulation in which effects of the random motion of the electrons are predicted to result from (i) the Doppler shift due to electron motion parallel to the direction of propagation, (ii) electron free paths extending over distances significant compared to the attenuation length, and (iii) variation of collision frequency with electron velocity. The results of a numerical study of the propagation of a right‐handed wave indicate that the first two of these effects are important in the region of cyclotron resonance even at moderate temperatures (e.g., in re‐entry plasmas) provided that the collision frequency is small compared to the signal radian frequency. Substantial reduction of the attenuation of a right‐handed wave in a plasma may be achieved by means of a magnetic field aligned parallel to the direction of propagation. The cyclotron frequency must be of the order of the signal radian frequency or larger and such that the enhanced attenuation arising from the electron random motion is avoided. The effectiveness of a given magnetic field in reducing the attenuation increases with decreasing ratio of collision frequency to signal radian frequency.