An annular fairing for covering the annular chamber end wall of a turbomachine combustion chamber, and in particular of an airplane turbojet. The fairing presents openings for passing fuel injectors that are supported by the chamber end wall. The fairing is subdivided into a plurality of adjacent sectors, each sector presenting inner and outer fastener edges capable of being fastened on either side of said chamber end wall. Each sector includes a lip on one of its side edges, which lip is connected to the remainder of the sector by a step, said lip being designed to over the side edge of the adjacent sector.