A specialized cannula and intraluminal cannula placement apparatus allow the insertion of an intraluminal cannula through a previously inserted standard I.V. catheter so that the intraluminal cannula extends beyond the end of a standard catheter. By using an intraluminal cannula of appropriate length, the intraluminal cannula may be used to bypass a flexure-caused obstruction in a vein during the administration of fluids in patients who are unable to cooperate with medical or veterinary procedures, most particularly with human infants, geriatric patients, and animals. Use of the specialized cannula and intraluminal cannula placement apparatus does not require removal of the previously placed I.V. catheter. The exterior diameter of the specialized cannula has a smaller diameter than the interior diameter of the previously placed standard I.V. catheter. A specially adapted seal seals the space between the inserted specialized cannula and a standard Luer hub of an I.V. catheter. In use, a health practitioner advances the specialized cannula through the standard I.V. catheter and into the vein with a pusher. When inserted, there is no extracorporeal extension to the hub of the standard I.V. catheter and the intraluminal cannula cannot be removed without simultaneous removal of the standard I.V catheter.