The instability of a field-aligned electron beam of finite width streaming through a uniform magnetized plasma is investigated. An earlier paper presented an analysis of the normal modes for electromagnetic waves in a ‘top hat’ beam– plasma system. The present paper extends the analysis to higher frequencies and different system parameters. Besides discussing the nature of the normal modes, the wave field variation within the beam region is studied. In doing this it is found that an electrostatic approximation is useful in describing the general form of the dispersion relation, specifically showing how the beam width controls the range of allowed solutions. The electrostatic approximation is shown to be good for most of the range of frequencies considered. When the electron gyrofrequency is greater than the electron plasma frequency, the theory predicts that the cold plasma upper-hybrid resonance band (Z mode) is stable to negative Landau damping. A criterion for applying this result to beam-plasma systems other than the ones investigated here is developed, and it is found that the effect should be more readily observable in laboratory experiments than in space plasmas.