The effect of a small amplitude, high frequency, magnetic field on cyclotron drift instabilities is investigated. An asymptotic expansion of a modified plasma dispersion function is used to obtain an approximate dispersion relation. The growth rate of the flute mode is increased, but it is possible to remove the instability if an appropriate condition is satisfied. The growth rate of the convective mode is decreased, but the region of instability is expanded. It is shown that the growth rate for the ion resonant mode is also reduced, but the instability still exists.