Method for complete combustion of a homogeneous mixture of air and fuel, - by means of a woven fabric membrane composed of inorganic precious metal fibers disposed upstream from a combustion side and downstream from a device that serves as a feed of the fuel/air mixture, and is permeable for the mixture, - having an entry side of the woven fabric membrane for the fuel/air mixture on the membrane side facing away from the combustion side of the membrane, - having an exit side of the membrane, facing away from the entry side of the latter, forming the combustion side, on which combustion takes place directly, and which takes part in flame ignition and stabilization thereof, - with generation of a planar and low flame field by means of the fuel/air mixture on the exit side of the woven fabric of the membrane, and - having additional openings in the membrane for additional fuel/air mixture passage and for generation of a flame field having higher separate flames having separate flame roots, - wherein the length of the flame on the additional openings is higher than in the area of the membrane without additional openings due to the exhaust velocity, - and wherein the flame roots of the higher flames are kept cool, in that the orifices of the additional openings of the membrane have an irregular configuration, characterized in - that the orifices of the additional openings furthermore projects beyond the exit side of the woven fabric, - the additional openings are configured as passage holes that connect the two sides of the membrane, whose orifices, forming the flame root, project out of the opening, in each instance, on the exit side of the woven fabric into the combustion chamber, forming their orifices - and that orifice configuration occurs by modification of the woven fabric in the form of fraying of the orifice edge. - by means of a woven fabric membrane composed of inorganic precious metal fibers disposed upstream from a combustion side and downstream from a device that serves as a feed of the fuel/air mixture, and is permeable for the mixture, - having an entry side of the woven fabric membrane for the fuel/air mixture on the membrane side facing away from the combustion side of the membrane, - having an exit side of the membrane, facing away from the entry side of the latter, forming the combustion side, on which combustion takes place directly, and which takes part in flame ignition and stabilization thereof, - with generation of a planar and low flame field by means of the fuel/air mixture on the exit side of the woven fabric of the membrane, and - having additional openings in the membrane for additional fuel/air mixture passage and for generation of a flame field having higher separate flames having separate flame roots, - wherein the length of the flame on the additional openings is higher than in the area of the membrane without additional openings due to the exhaust velocity, - and wherein the flame roots of the higher flames are kept cool, in that the orifices of the additional openings of the membrane have an irregular configuration, characterized in - that the orifices of the additional openings furthermore projects beyond the exit side of the woven fabric, - the additional openings are configured as passage holes that connect the two sides of the membrane, whose orifices, forming the flame root, project out of the opening, in each instance, on the exit side of the woven fabric into the combustion chamber, forming their orifices - and that orifice configuration occurs by modification of the woven fabric in the form of fraying of the orifice edge.