Sleeve designed to be connected to a rotary hub of an aircraft, said sleeve in span extending, on one hand, in a longitudinal direction in span from a first extreme zone to a second extreme zone and, on the other hand, in a transverse direction between two transverse edges (15, 16), said two transverse edges (15, 16) being a leading edge and a trailing edge, said sleeve comprising a first upper surface and a first lower surface, said sleeve being defined by a first length L equal to a distance between said first extreme zone and said second extreme zone in said longitudinal direction, said sleeve being formed by a succession of first profiles located in planes parallel to a transverse plane (Pyz) perpendicular to said longitudinal direction in span, each first profile being defined in a plane parallel to said transverse plane (Pyz) by a thickness h equal to a maximum distance between said first upper surface and said first lower surface, characterised in that said sleeve includes at least one protuberance arranged on at least one of said transverse edges (15, 16), each protuberance being integral with said sleeve, each protuberance including a second upper surface and a second lower surface, each protuberance extending transversely from said transverse edge (15, 16) on which said protuberance is arranged, to a transverse end of said protuberance where said second upper surface and said second lower surface meet, each protuberance being configured so as to improve the aerodynamic behaviour of said sleeve both when said sleeve impacts an air flow with said leading edge and with said trailing edge, each protuberance being defined by a second length L' equal to a distance between a third extreme zone and a fourth extreme zone of said protuberance in said longitudinal direction, said second length L' being comprised between 0.5 and 1 times said first length L of said sleeve, each protuberance being formed by a succession of second profiles located in planes parallel to said transverse plane (Pyz), each second profile being defined by: - a height h' equal to a distance between said second upper surface and said second lower surface, said height h' being comprised between 0.2 and 0.6 times said thickness h of said sleeve, - a width l 'equal to a distance between said first profile and said transverse end in said transverse direction, said width l ' being equal to 0.5 to 2 times said height h', - non-zero connecting radii between said first profile and said second profile, and - a radius of curvature of said transverse end of said protuberance between said second upper surface and said second lower surface greater than a minimum radius R mini. - a height h' equal to a distance between said second upper surface and said second lower surface, said height h' being comprised between 0.2 and 0.6 times said thickness h of said sleeve, - a width l 'equal to a distance between said first profile and said transverse end in said transverse direction, said width l ' being equal to 0.5 to 2 times said height h', - non-zero connecting radii between said first profile and said second profile, and - a radius of curvature of said transverse end of said protuberance between said second upper surface and said second lower surface greater than a minimum radius R mini.