The invention relates to a premix burner of the multi-cone type for a gas turbine that includes a plurality of shells which are arranged around a central burner axis and are parts of a virtual, axially extending common cone, which opens in a downstream direction, whereby said parts are displaced perpendicular to said burner axis such that a tangential slot is defined between each pair of adjacent shells. The flame front of such a burner is stabilized by providing a virtual common cone with a cone angle, which varies in axial direction.