Realizing sufficiently high conversion is essential for industrial application of catalytic decomposition of biomethane to hydrogen and nanocarbon. This suggests that the reaction has to be performed at an equilibrium-required high temperature. Choice of the most investigated Ni as well as Co catalyst that deactivates rapidly at high temperature was excluded, and focus was laid upon less active but more environmentally-friendly Fe-catalyst. Systematical investigation on activity and stability of Fe-alumina catalyst was carried out in a horizontal quartz reactor at conditions of temperatures= 670-780 degrees C, gas flow rates= 10-80 ml/min and CO2 concentrations= 0-5 vol.%. Higher than 60% methane conversions with the weight ratios of the solid product to packed catalyst >10 can be obtained at temperatures > 700 degrees C. Increasing gas velocity reduces catalytic stability but the same maximum activity can be obtained over a wide range. Addition of CO2 into feed gas increases the temperature where the catalyst begins activation and provides an identical stable conversion. Pre-reduction of the catalyst using hydrogen is not necessary. Produced nanocarbon fibers were characterized by using various techniques including TG, XRD, Raman, SEM and TEM, and confirmed to be highly crystalline and have graphitic structure.