Ah&a&--At arc discharge in a methane ambient, the heat-up of the anodic and cathodic patches can under certain conditions be high enough to initiate gas pyrolysis. Then carbon deposits grow onto the electrodes within the patches. The anodic deposits have a column shape, while the cathodic deposits are radical growths of a hemispherical nature. Because the temperature is relatively low for arc discharge within the patches, the arc ion supply and the electric current limitation by means of the power supply are reasons why we have termed the process abnormal arc discharge. The growth of carbon deposits within the arc patches is observed for the first time and includes three stages, nucleation, growth along the shortest path between the anode and cathode and growth in a direction subtending an angle to the shortest path between the anode and cathode. An analysis of the thermal balance at the anodic and cathodic patches has been conducted, while the parameters of the processes influencing this phenomenon have also been discussed. The growth process observed is presented by a series of consecutive photos. At a work gas pressure of P = 3~Pa, an Hz/CHj ratio of 90110 and a discharge power of 36 W, the growth rate is 15 mm/h. In accordance with the classification for carbon obtained at methane pyrolysis, the growths are considered as "compact silver grey carbon.