This implant (1) has a frame (2) and a membrane (3) covering this frame； —the frame (2) has: —an elongated base portion (5) formed by two curved or chevron branches being connected to connecting areas (7) of the implant (1) for connecting to the annulus of the mitral valve (100)； —a longitudinal hoop (8) extending in a plane substantially perpendicular to the plane in which extends said base portion； —the membrane (3) is flexible and extends from one branch to the other while passing near the hoop (8), this membrane being connected to said branches without being stretched between these branches and this hoop so that the two thereby formed lateral portions (3a) of the membrane (3) on both sides of the implant are able to adopt either a concave shape, outwardly convex, or a recessed shape, outwardly concave.
