The burner of a gas turbine includes a swirl generator and, downstream of it, a mixing tube. The swirl generator is defined by at least two walls facing one another to define a conical swirl chamber and is provided with nozzles arranged to inject a fuel and apertures arranged to feed an oxidiser into the swirl chamber. The burner includes a lance which extends along a longitudinal axis of the swirl generator and is provided with side nozzles for ejecting a fuel within the burner. The side nozzles have their axes inclined with respect to the axis of the lance and can be positioned along the axis of the burner.