A support arm (13) is intended to be installed in a radial position in an afterburner device of a bypass turbojet. The device comprises first and second inner annular casings defining a passage for a primary flow and an outer annular casing defining together with the first inner annular casing a passage for a secondary flow. The arm (13) comprises a monobloc structure made of composite material including two integral walls (14, 15), on the one hand, designed to define a groove (16) having a substantially V-shaped profile and, on the other hand, including first end parts (17) joined together and adapted to define a foot (18) and second end parts (19) adapted each to define at least one flange (20, 21) intended to be positively connected to the outer annular casing.