The invention relates to a method of cleaning the surface of a material (4) that is coated with an organic substance. The inventive method is characterised in that it comprises the following steps, consisting in: introducing the material (4) into a treatment chamber (2), having a pressure of between 10 mbar and 1 bar therein, which is supplied with a gas stream containing at least 90 volume percent of oxygen; and generating a plasma by passing an electric discharge between the surface of the material and a dielectric-covered electrode (5a, 5b, 5c, 5d, 5e, 5f, 5g) in order to break down the organic substance under the action of the free radicals O thus produced. The invention also relates to an installation (1) that is used to carry out said method.