A method and construction for treatment of sludge from waterworks and wastewater treatment plants is disclosed. The method for treatment of sludge from waterwork or wastewater treatment plant, comprising precipitated inorganic chemical coagulants and precipitated organic substances, comprises adding an acid to the sludge in such a way that a first sludge mixture with low pH is received. The first sludge mixture includes the inorganic chemical coagulants in solution and the organic substances. The sludge mixture is pumped, via heat exchangers to a pressure tank. An obtained first concentrate is fed to at least one membrane filtration process in which a second concentrate and a first permeate are obtained.