In order to use so-called gray water for the flushing of toilets, for example in a conveyance such as a passenger aircraft, the gray water is passed through at least one filter, preferably through a coarse filter followed by a fine filter, into a treatment tank where it is anodically oxidized. The rinsing is performed by a pump that may be a rotary pressure pump or a piston cylinder pump. The pump passes the processed or oxidized water through an excess pressure valve and through at least one spray nozzle into a toilet bowl.