A torque transmitting guiding catheter adapted for insertion into vascular vessels with a body and a method for its construction is disclosed. The guiding catheter includes a flexible tubular member surrounded by a pair of torque transmitting layers that are formed of a flat braided material. A flexible (plastic) casing that initially is applied as a viscous material impregnates and encases the torque transmitting layer to hold them in place and eliminate their rough edges. The ends of the torque transmitting layers are soldered using a radiopaque solder to enhance the catheter's visibility within a body. The tubular member is also folded about the distal end of the catheter over the distal extremity of at least one of the torque transmitting layers to provide a smooth and soft distal catheter tip. The formed catheter has a flexible curving distal tip. The tip's shape memory is enhanced by at least partially curing the casing material while the tip takes the form of its desired final shape.