A new mechanism capable of strongly modulating an intense relativistic electron beam using two cavities was found recently. The frequency of the modulated intense relativistic electron beam (IREB) depends on the time it takes an electron to transit the distance between the two cavities. This transit time can be varied by changing the distance between the two cavities or by changing the propagation velocity of the electron beam. It is shown, in this paper, that by varying the intensity of a magnetic field located between the two cavities the drift velocity of the electrons in the IREB is changed, influencing the frequency of the IREB modulation. In a typical experiment a modulated IREB with power ∼5×109W was generated. The frequency of modulation was varied by ∼34% using an auxiliary small magnetic field coil.