A dual lumen hemodialysis catheter. The catheter includes a tube having a circular external cross section which is rotatably received within a fitting. The fitting may be attached to the patient by sutures or the like and rotatably mounts the tube of the catheter. Stop means are provided on opposite sides of the fitting preventing the tube of the catheter from moving longitudinally relative to the fitting. The catheter may be rotated relative to the fitting in order to readjust the rotational position of the tube inside the patient's blood vessel without longitudinal movement of the tube. The catheter is cut off at its distal end perpendicularly to the length of the tube in order to define the mouth of one lumen. The tube is tapered from the cut off distal end to a point proximal of the distal end, said point being approximately 3 cm from the distal end. The taper of the tube defines at least a portion of the mouth of the second lumen.