Electrostatic electron cyclotron harmonic waves are driven by an excess electron kinetic energy perpendicular to the magnetic field. If the anisotropy of the velocity distribution is transient, the propagation characteristics of the anisotropy-driven waves change in time. The long-time behavior of the waves is determined by the dispersion relation corresponding to the final velocity distribution. A model case is studied, within the framework of linear theory, for 3/2 electron cyclotron harmonic waves in the relaxation stage of a bi-Maxwellian velocity distribution. It is shown that the dominant propagation angle changes from about 60¿ in an unstable state to about 80¿ in an isotropic state. Because of strong Landau damping, the most unstable wave in the instability cannot be a dominant wave after the relaxation. Since this result may be true for other velocity distribution models, it implies that great care should be taken in considering a wave model which requires a long lifetime for some of the waves involved.