The valve comprises a valve seat (6) and a valve body(7) with a circular diaphragm (70). The valve body (7)is arranged over the valve seat (6) in order to closethe latter sealingly when it bears on the valve seat(6). The valve seat (6) and the valve body (7) haveopenings (64, 65, 71, 73) which are offset relative toone another and which form a free passage when thediaphragm (70) of the valve body (7) lifts. Thediaphragm (70) of the valve body (7) has elongateopenings (71) which are uniformly distributed along acircle in the periphery of the diaphragm (70), thecircle having approximately the same center point asthe diaphragm (70). The elongate openings (71) areseparated from one another by webs (72), the diaphragm(70) being designed to be weaker in the area adjacentto these webs (72). It can be produced simply andinexpensively, is reliable in its use, and scarcelydeforms at all even in the case of considerablevariations in temperature. It is suitable in particularfor use in breast shield sets, for reducing the deadvolume.