In a premixing burner (1) which essentially consists of a mixing section (3) and a downstream combustion section (13), an ignition zone (9) being placed intermediately between the two sections, a fuel (5) and combustion air (4) are introduced at the head side of the mixing section (3) to form a mixture. At the end of the mixing section (3), the fuel/air mixture (6) ignites in the region of the ignition zone (9), specifically in such a way that no backflow zone is formed on the axis (12) of symmetry. Self-ignition and flashback are prevented by the high velocity of the mixture (6) in the mixing section (3). A conical reaction zone (11) is produced by the temperature differences between wall boundary layer and core of the hot-gas flow (15) inside the combustion section (13).