A beverage machine, in particular a coffee machine, prepares a beverage using water supplied via a fixed water connection to a hydraulic part arranged in the beverage machine and outputs the beverage at an outlet of the beverage machine. Maintenance is simplified by the fact that the beverage machine is provided with a cartridge holder which is accessible from the outside and into which a cartridge can be inserted in an exchangeable manner, the cartridge includes a cartridge connection on the inlet side and a cartridge connection on the outlet side, via which, in the inserted state of the cartridge, water supplied to the beverage machine via the fixed water connection flows through the cartridge and is thereby filtered and/or enriched with additives.