Method for the purification of water from aquaculture system plants, comprising the steps of: a) adding ozone (12) to at least a part of a flow of water (11) from an aquaculture plant b) allowing ozone and water to be (thoroughly) mixed in a mixing zone (14) c) allowing the mix of water and ozone a contact time sufficient to create microflocks d) charging the mix of water and ozone (15) into a flotation tank (16) e) creating air bubbles at the lower end of the flotation tank (16) f) controlling a flow rate through the system which allows a desired retention time in the flotation tank (16) g) removing floated particles (18) from the top surface of the liquid in the flotation tank (16) and h) discharging purified water (21) from the flotation tank through a low end discharge opening (164). An apparatus for conducting the method is also contemplated.