The door system consists of a door frame (1) and at least one door leaf, (2) as well as a door drive (3) with a control unit. The door leaf (2) is equipped with a hand vein scanner (4) for detecting the hand vein profile when a hand is held a distance in front of the hand vein scanner (4) for the purpose of recognizing the user. A programmable computer unit (5) with a memory element, in which a plurality of user hand vein profiles can be stored, is housed in the interior of the door leaf (2). A hand vein profile is compared to the hand vein profiles stored in the memory element of the computer unit (5) and, depending on a match, the door is opened or not. The computer unit (5) is programmed and supplied with power via a network interface (10) that terminates in the edge (8) of the door leaf or the peripheral area (9) and is the only interface between the door leaf (2) and the door frame (1), other than the signal cable (6) for the control unit for the door drive (3). The computer unit (5) can be programmed by temporarily connecting an external computer (7) to this network interface (10). The network interface (10) is also used for connecting a power supply for the computer device (5).