Abstract: A method of treating a methane residue in a gas mixture at a temperature lying in the range 200° C. to 500° C. and including at least methane at a concentration lying in the range 50 ppm to 2500 ppm and oxygen at a concentration lying in the range 0.5% to 12% by volume. According to the invention, the methane residue is treated by a plasma having energy density lying in the range 15 J/L to 100 J/L generated in a plasma reactor by applying a high voltage electrical signal between an internal electrode and an external electrode of the plasma reactor, the external electrode being cylindrical in shape and surrounding the internal electrode, and at least one of the electrodes being covered in a dielectric material to create a dielectric barrier discharge in the gas mixture and convert part of the methane residue into carbon monoxide.