An endoprosthesis composed of a first member constituting a prosthesis socket provided interiorly with a chamber presenting a receiving surface, a second member constituting a prosthesis head arranged to be inserted into the socket to be received in the chamber and presenting a surface engaging the receiving surface when the head is received in the chamber, and a shaft firmly connected to the head. The head is arranged to be inserted into the socket by insertion movement, relative to the socket, from an insertion position to an inserted position, and to be rotated, relative to the socket, between the inserted position and an installed state. The socket presents a boundary edge formed to present at least one corner which encloses the head when the head is in the installed state and which defines a deformation, and the surface of the head is provided with a groove extending in the direction toward the shaft and defining a deformation, the depth of the groove being approximately equal to the constriction presented to the insertion opening by the corner.