In order to keep the opening for insertion of a catheter as small as possible a splittable catheter insertion tube (1) which surrounds the puncturing cannula coaxially and whose outer diameter (d2) at the insertion end into the blood vessel (3) is the same as or almost the same as the outer diameter (d1) of the catheter (4) and which is split over its entire length with a catheter (4) guided via a mandrin (5) or with a catheter (4) having a correspondingly designed and dimensioned catheter tip (9, 11) as the guide member by stepwise simultaneous insertion of the catheter (4) and retraction of the catheter insertion tube (1) and, finally, is completely removed during placement of the catheter (4), is used. <IMAGE>
