A gasket for a hemostasis valve includes an annular wall, a membrane, a central protrusion on the membrane, and a plurality of ligaments attached to the central protrusion extending radially to the annular wall. The membrane, central protrusion, and ligaments are divided by slits into a plurality of flaps, with each flap bounded along an outer circumferential edge by the annular wall, along an inner circumferential edge by the central protrusion, and along its radial edges by segments of the ligaments. Two such gaskets can be arranged, back-toback, in a hemostasis valve. To facilitate such assembly, each gasket can include a plurality of positioning protrusions extending axially and a plurality of positioning recesses set into a circumferential surface, with the protrusions and recesses having complementary shapes for proper interconnection and fit between gaskets.