A heat exchanger with a leakage vent. A fully brazed heat exchanger has an arrangement preventing the two media inside the heat exchanger from mixing in case of leakage. The heat exchanger includes plates having a pattern of grooves and inlet and outlet connections. The plates are placed in a pack and brazed together so as to form separate channels for two media between alternating pairs of plates. A separation zone is created around the connection so as so block off the medium that is not to reach the respective connection. The other medium can flow on by. A leakage vent to the exterior is provided in the separation zone so as to allow detection of any leakage.