A tubing assembly for manufacture for a catheter of the type having an inner tubular member defining a lumen, an outer tubular member surrounding said inner member, and a support member mounted between the tubular members to provide rigidity to the flexible catheter. The support member comprises a high tensile strength wire braid, and in the preferred embodiment comprises a stainless steel wire braid which has been tempered or hardened. This higher tensile strength affords significantly greater kink resistance to the flexible catheter. One wire braid has a tensile strength in the range of 300 to 425 kpsi and a braid density of approximately 40 pic. The high tensile strength wire braid has the disadvantage of tending to flare out at its free ends. Therefore, means are provided for preventing the flaring of the wire braid during manufacture of the tubing assembly. One means includes adhesive applied over the free ends. Another means includes a restraining sleeve applied over the free ends.