A method for backwashing a filter for filtering liquids, said filter being made up of a granular material that can be fluidized, by means of at least one backwashing cycle intercalated between filtering cycles, which comprises: - injecting a clean liquid through said filter in a first direction opposite the filtering direction; - distributing said clean liquid homogenously throughout the entire section of said filter by means of at least one backwashing inlet; and - discharging said liquid through at least one backwashing outlet; wherein during said backwashing cycle, a cleaning flow rate is injected in a first step through the backwashing inlets, and a terminal flow rate is injected in a final step of said cycle trough the same inlets; and characterized in that the cleaning flow rate entrains the contaminants retained in the granular material to the backwashing outlets for discharge from the filter, and the terminal flow rate displaces a fraction of the volume of liquid contained in the granular material to discharge it, thus preparing the filter for restarting the filtering cycle; said terminal flow rate being selected to provide a stream of clean liquid that is displaced through the granular material at a speed less than the sedimentation rate of the bottom fraction of the grain size distribution forming the granular material of the filter; and wherein said cleaning flow rate fluctuates during the backwashing cycle between at least two values: - a higher cleaning flow rate that is injected through the granular material providing a stream that is displaced at a speed equal to or greater than the sedimentation rate of the top fraction of the grain size distribution of the granular material of the filter and less than the upward entrainment rate of the bottom fraction of the grain size distribution forming the granular material of the filter to the backwashing outlet; and - a lower cleaning flow rate, that is injected through the granular material providing a stream of clean liquid that is displaced through the granular material at a speed equal to or greater than the sedimentation rate of the bottom fraction of the grain size distribution forming the granular material of the filter; wherein said fluctuation being repeated a plurality of times during said backwashing cycle. - injecting a clean liquid through said filter in a first direction opposite the filtering direction; - distributing said clean liquid homogenously throughout the entire section of said filter by means of at least one backwashing inlet; and - discharging said liquid through at least one backwashing outlet; - a higher cleaning flow rate that is injected through the granular material providing a stream that is displaced at a speed equal to or greater than the sedimentation rate of the top fraction of the grain size distribution of the granular material of the filter and less than the upward entrainment rate of the bottom fraction of the grain size distribution forming the granular material of the filter to the backwashing outlet; and - a lower cleaning flow rate, that is injected through the granular material providing a stream of clean liquid that is displaced through the granular material at a speed equal to or greater than the sedimentation rate of the bottom fraction of the grain size distribution forming the granular material of the filter;