A burner of a gas turbine including a reaction chamber and a plurality of jet nozzles opening into the reaction chamber is provided. Fluid is injected through an outlet into the reaction chamber by the jet nozzles using of a fluid stream wherein the fluid is burned into hot gas in the reaction chamber. An annular gap is disposed about the fluid stream for at least one jet nozzle so that a part of the hot gas is drawn out of the reaction chamber and flows opposite the fluid flow direction into the annular gap and is mixed with the fluid stream within the jet nozzle. The ring gap is formed by means of an insert tube, and wherein the insert rube includes a thickening at the upstream end. A method for stabilizing the flame of such a burner of a gas turbine is also provided.