A filtering system comprising an inlet (11) for liquid to be filtered and an outlet (9) for filtered liquid, as well as filtering means, which system is characterized in that the filtering means, placed in series comprise: a first filter (2) comprising activated carbon with the capability to also remove particles that are larger than approximately 0.5 .mu.m; an ultrafiltration membrane (5) for the removal of particles that are larger than approximately 0.02 .mu.m; a post-treatment filter (14) of activated carbon, optionally provided with a microfiltration membrane (13), wherein the system also comprises a vessel (6) for filtered water located between the ultrafiltration membrane (5) and the post-treatment filter (14), with the option of using the filtered water from the vessel for back-flushing the ultrafiltration membrane (5).