Abstract: In this article, we study the suppression of the multipactor phenomenon on a dielectric surface by a resonant static magnetic field. A homemade Monte Carlo algorithm is developed for multipactor simulations on a dielectric surface driven by two orthogonal radio frequency (RF) electric field components. When the static magnetic field is perpendicular to the tangential and normal RF electric fields, it is shown that if the normal electric field lags the tangential electric field by pi/2, the superposition of the normal and tangential electric fields will trigger a gyro-acceleration of the electron cloud and restrain the multipactor discharge effectively. By contrast, when the normal electric field is in advance of the tangential electric field by pi/2, the difference between the normal and tangential electric fields drives gyro-motion of the electron cloud. Consequently, two enhanced discharge zones are inevitable. The suppression effects of the resonant static magnetic field that is parallel to the tangential RF electric field or to the normal RF electric field are also presented.