A swing arm for a suspension of a vehicle comprises a substantially transversely outer arm portion having a free end for mounting of a support for supporting a wheel of the vehicle and a substantially transversely inner arm portion with a first branch and second branch. The first branch is substantially aligned with the outer arm portion and has a free end for mounting of a first connector for connection to a body of the vehicle, and the second branch extends along an arched path towards a rear part of the vehicle and has a free end for mounting of a second connector for connection to the vehicle body. A single-sheet metal piece includes a main portion having an open section and at least one secondary portion arranged in an edge zone of the swing arm, having a closed section, and formed by at least one strip of the metal piece folded onto the main portion and firmly secured with a free edge of the strip to the main portion. A method for manufacturing the swing arm comprises steps of obtaining the main portion by stamping of the metal piece, folding the strip of the metal piece so as to obtain the secondary portion, and firmly securing the free edge of the strip to the main portion.