Adapter (26, 26′) for connecting a windscreen wiper blade (12) to a driving arm (14), the adapter (26, 26′) having a ‘U’-section formed by a base and two flanks (42a, 42b) delimiting a housing (45) in which: at least one (42a) of the flanks is formed by at least two walls (42aa, 42bb) separated from one another by at least one cavity (63, 64), and at least one protuberance (60) is connected to at least one of the walls (42aa, 42ab, 42ba, 42bb) and extends at least in part inside said housing (45).