A method of fabricating an aircraft landing gear rocker beam comprising a body having a clevis (24) with two lugs (19, 21) parallel to a direction that is radial relative to the body, the method comprising the steps of: forming a first mandrel; applying one or more first braided fiber layers (11) on the first mandrel; fitting a second mandrel element on the assembly as constituted in this way, the second mandrel element extending between the two lugs (19, 21) of the clevis (24) that is to be formed; applying one or more second braided fiber layers (17) on the assembly as constituted in this way; injecting resin into the various layers (11, 17) and polymerizing the resin; and machining the resulting workpiece blank in order to cut away a region of the second braided layers (17) in order to separate the two lugs (19, 21) of the clevis (24) from each other.