A hemostasis valve is provided for catheters or the like, comprising an elastomeric partition valve secured in a housing. A linear slit extends through the partition valve between the major faces thereof. By this invention, the slit defines a line at each major face, with the respective lines at the major faces being in non-alignment and thus defining an angle with respect to each other. The slit defines at least one generally helical slit section between the lines of the major faces, within the partition valve. Such a partition valve exhibits better sealing characteristics over a wide range of diameters of catheters, leads, or the like penetrating the partition valve, as well as other advantages.