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 the parts are displaced perpendicular to the burner axis such that a tangential slot is defined between each pair of adjacent shells. A disadvantageous transition piece between the shells and a downstream mixing tube is avoided by bordering the downstream ends of the shells by intersecting planes, which are defined by intersecting the shells with a virtual coaxial cylinder of a predetermined radius.