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The instabilities of an infinitely long and azimuthally symmetric annular electron beam propagating along an external applied magnetic field are investigated using the fluid-Maxwell theory. Unlike the treatment in the conventional diocotron instability, full electromagnetic perturbations have been emphasized and no approximation has been made such as kÂ¿~ 0 and Â¿ ~ckÃ in the macroscopic cold fluid description. There have been found two distinct and different instabilities depending on the value of doppler-shifted eigenfrequency Â¿-ckÃ. The diocotron instability dominates in the low frequency region while cyclotron resonance perturbation plays a major role in the high frequency domain. In the case of a sharp boundary density profile, the growth rates versus different wavenumber k are shown for both instabilities in the beam parameters of out interest.