A premix burner includes a vortex generator (30) for combustion air stream (15), devices (17, 17a, 17b, 31-38, 41-48) to inject fuel into the combustion air stream (15), and tangential air ducts (19, 20). The combustion air (15) enters the cone cavity (14) of the vortex generator (30) via the air ducts. The injection of the fuel into the combustion air is done asymmetrically by injection devices (17, 17a, 17b, 31-38, 41-48). At least one of the injection devices (5) is arranged on a fuel lance (3) that extends into the vortex chamber.