A sealing device between a rotor part (8,18,38b;35,36) and a stator part (9,43;440) of an aircraft gas turbomachine, wherein gas is to circulate from upstream to downstream, the rotor part being adapted to rotate relative to the stator part about an axis, the sealing device comprising at least one covering made of abradable material: - secured to the stator part (9,43;440), and - adapted to cooperate with at least two respectively axially upstream and downstream seal lips (40a,40b), radially projecting over an extreme portion of the rotor part (8,18,38b;35,36), the covering and said at least two seal lips (40a,40b) respectively radially having at least two axially upstream and downstream free axial sealing surfaces (48a,48b), respectively, and respective free ends (50a,50b), the free end of the downstream seal lip and the downstream free axial sealing surface being located at radial positions which are each further away from the axis than the free end of the upstream seal lip and than the upstream free axial sealing surface, and, axially upstream of said at least two seal lips (40a,40b) with respect to the direction of the gas flow, the sealing device comprising a circumferential wall which radially extends beyond the upstream free axial sealing surface of said covering, by penetrating radially into the gas flow, thereby forming a substantially transverse obstacle to the flow of gas coming from upstream, characterized in that, to create, at the free end of the upstream seal lip, a detachment of the circulating gas, the circumferential wall is defined by a difference in level formed on said covering, projecting radially with respect to a free upstream axial surface (47a, 48c, 72a) of the sealing device, which free upstream axial surface (47a, 48c, 72a) is adjacent to the circumferential wall, axially, upstream with respect to the circumferential wall. - secured to the stator part (9,43;440), and - adapted to cooperate with at least two respectively axially upstream and downstream seal lips (40a,40b), radially projecting over an extreme portion of the rotor part (8,18,38b;35,36), the covering and said at least two seal lips (40a,40b) respectively radially having at least two axially upstream and downstream free axial sealing surfaces (48a,48b), respectively, and respective free ends (50a,50b), the free end of the downstream seal lip and the downstream free axial sealing surface being located at radial positions which are each further away from the axis than the free end of the upstream seal lip and than the upstream free axial sealing surface, and, axially upstream of said at least two seal lips (40a,40b) with respect to the direction of the gas flow, the sealing device comprising a circumferential wall which radially extends beyond the upstream free axial sealing surface of said covering, by penetrating radially into the gas flow, thereby forming a substantially transverse obstacle to the flow of gas coming from upstream, characterized in that, to create, at the free end of the upstream seal lip, a detachment of the circulating gas, the circumferential wall is defined by a difference in level formed on said covering, projecting radially with respect to a free upstream axial surface (47a, 48c, 72a) of the sealing device, which free upstream axial surface (47a, 48c, 72a) is adjacent to the circumferential wall, axially, upstream with respect to the circumferential wall.