In a transseptal crossing needle device for inserting an outer sheath through a septum, an inner dilator sheath is received within the outer sheath and a needle having a curved end portion adjacent a tip of a tip portion of the needle is provided, the needle being received in the inner dilator sheath. The needle tip portion comprises an angled transverse end surface terminating at said tip and slanting away from an inner concave curved wall of said inner sheath curved by the needle curved end portion, the needle tip being spaced not only away from said inner concave curved wall of said inner sheath but also away from an inner convex curved wall of said inner sheath opposite said concave wall to reduce or eliminate skiving of material from the concave and convex inner walls of the inner sheath.