Abstract: In a glass fiber forming unit including a hollow-cylinder-shaped rotating spinner having (a) a bottom, (b) a surrounding wall with a number of molten glass projecting orifices, and (c) an upper annular flange extending inwardly from the upper edge of the surrounding wall; and an attenuating blast burner with jet flame orifices for attenuating primary filaments formed at the tips of transition cones of molten glass projecting from the rotating spinner into secondary filaments, the improvement comprising the jet flame orifices in the attenuating blast burner being so positioned that, for each jet flame from each jet flame orifice, only an outer cone of flame is in contact with the lower portion of the outer surface of the surrounding wall of the hollow-cylinder-shaped rotating spinner where the speed of the outer cone of flame is such as to not break the transition cone of molten glass, and a heating burner disposed inside the upper annular flange of the hollow-cylinder-shaped rotating spinner for jetting a fla