A unit fuel injector (10) is used to inject fuel into the combustion chamber of an internal combustion engine. This is accomplished by opening a valve element (28) counter to a valve prestressing force by means of increasing a system pressure. Moreover, the system pressure is raised to a value above a normal valve opening pressure, so that the valve element opens for a main injection counter to the valve prestressing force. While the system pressure is being raised, the valve prestressing force is also increased, in such a way that a valve closing pressure that is increased because of the increased valve prestressing force is always below the system pressure. The system pressure is then lowered and to a value below the valve closing pressure, so that the valve element closes. Next, the system pressure is increased again, so that the valve element opens for a postinjection, at a valve opening pressure that is increased because of the increased valve prestressing force. Finally, the system pressure is lowered again, and the valve prestressing force is lowered as well, so that the valve element (28) closes.