In the premix combustion of liquid fuel in a burner without premixing section, there is formed in the interior (14) of the burner a conical liquid fuel column (5) which widens in the direction of flow and which is surrounded by a rotating combustion air flow (15) which flows tangentially into the burner. Ignition of the mixture takes place at the outlet of the burner, a backflow zone (6) being formed in the region of the burner mouth. The burner itself consists of at least two hollow part cone members (1, 2) positioned on one another, which have a cone inclination which increases in the direction of flow. The part cone members (1, 2) are staggered in relation to one another, as a result of which tangential air inlet slots (19, 20) are formed. A nozzle (3) placed on the burner head ensures the injection of the liquid fuel (12) into the interior (14) of the burner.