A labyrinth seal for a turbine engine, comprising a rotor element rotating about an axis of rotation, and a stator element extending around the rotor element, the rotor element comprising a series of annular lips extending radially outwards and surrounded by at least one abradable element carried by the stator element, each said annular lip comprising an inner peripheral body portion, an outer peripheral body portion and an upstream annular face for impact of an air flow during operation, at least one lip of said series of annular lips having, looking from said upstream annular face, a first annular cavity with a concave rounded cross-section on its inner peripheral body portion and a second annular cavity with a concave rounded cross-section on its outer peripheral body portion, wherein the radius of curvature of the first cavity is between 0.5 mm and 2 mm, and the radius of curvature of the second cavity is between 0.8 mm and 2.5 mm.