A turbine shroud ring sector for a turbomachine supported at the upstream end by a downstream support of a turbine casing with circular sliding including a first stop able to collaborate with a second stop borne by an element of the turbomachine adjacent to the shroud ring in order to immobilize the shroud ring circularly is disclosed. The sector includes, on an end facing the element, a recess able to allow the second stop to pass to come into contact with the first stop. The recess is cut substantially in the form of a rectangle having, at the bottom of the recess, corners that are rounded in a circular arc of radius r. The bottom of the recess has a convex shape tangential to the circular arcs of the rounded corners and with a curvature that evolves between a radius of curvature r where it meets the rounded corners and a radius of R, greater than the radius r, at a point situated between the two rounded corners.