Maser cyclotron instability is studied in the case of interaction between a weakly relativistic hot loss-cone-like component and a cold-cool plasma, for a wide range of parameters applying to natural or artificial beam-plasma phenomena. We focus on the relativistic mode lying just below the electron gyrofrequency, which appears to couple to ordinary and Z modes. The semirelativistic dispersion relation is numerically solved in a number of cases, showing that the relativistic mode is much more easily excited than the usual upper X mode (f>fce), and that it generally retains the highest extraordinary mode growth rate, dominating over the O mode for very small (1) values of fpe/fce. This mode is therefore expected to prevail, at least locally, in the source region. The width of the instability range is found to be mostly determined by the ratio nhot/ncold, which must typically lie between 1 and 100. When nhot/ncold<10, Tcold needs in addition to be smaller than 0.2 Thot. Specific signatures of modes and implications for auroral kilometric radiation are derived. ¿ American Geophysical Union 1993