Abstract: The present invention relates to a process for the purification of waste water, in particular for the continuous purification of waste water in papermaking, where waste water to be purified is fed to an anaerobic reactor (12), the waste water is contacted, in the anaerobic reactor (12), with anaerobic microorganisms in order to degrade contaminants present in the waste water, and the purified waste water is discharged from the anaerobic reactor (12), where at least some of the waste water is subjected to a pressure-release flotation step (30) before being supplied to the anaerobic reactor or after being discharged from the anaerobic reactor, in order to delime the water to at least some extent Furthermore, the present invention relates to a device which is suitable for carrying out the process according to the invention.