A method for purifying sludge suspected of containing heavy, toxic and/or precious metals in order to extract them, the sludge being suspended in an aqueous solution and together forming a mass to be treated. FeCl.sub.3 is mixed with the mass, until an acidic pH of the solution is obtained. (CO.sub.2H).sub.2 and NH.sub.4Cl are then mixed with the mass until metal pro-chelates are formed. Mixed alkali sulfides are then mixed with the mass until a solution with a very basic pH is obtained, to form colloidal complex iron chelates, which trap the metals. The solution is neutralized by adding an acid, until alkaline-ferrous sulfides and hydroxides containing the metals are precipitated. The mass is then centrifuged to form from the mass a liquid phase and a solid phase, the solid phase containing the alkaline-ferrous sulfides.