The invention provides a catheter for placement within a vessel of a patient. The catheter comprises an elongated catheter body, a septum extending longitudinally through the interior of the catheter body from the dividing the interior of the catheter body into a first lumen and a second lumen. Each lumen has curved or angled internal walls at the distal end of the catheter that terminate at ports located on opposing sides of the catheter body. The invention also provides a method for exchanging fluids in a patient comprising the step of positioning the catheter of the present invention in communication with a fluid-containing vessel of a patient. The method is particularly well-suited for hemodialysis, plasmapheresis, and other therapies which require removal and return of blood.