The electron cyclotron maser instability is analyzed for the following case, in which a relativistic monoenergetic electron beam is injected into a background plasma, but the beam direction is initially oblique to the ambient magnetic field. We consider that the electron plasma frequency is comparable to the electron cyclotron frequency associated with the external magnetic field and study the situation: (1) the background plasma density n0 is much larger than that of the suprathermal electron ns and (2) n0s. The relativistic effects destablized the o and x mode with frequencies respectively in the vicinity of the fundamental and the second harmonic of the electron cyclotron frequencies. The growth rates of both modes are computed and discussed.