To provide a connection member at low cost which is used between a cracking tube of a cracking furnace and a cooling tube of a cracked-gas cooler.

The cooling tube 2 is formed as a double tube formed of the inside tube 3 and the outside tube 4, and between those tubes, a cooling clearance 5 is provided. The cooling clearance 5 is connected to a feed chamber 6 for feeding a coolant, and the cracking-tube 1 is connected to a transition member 14 forked in its end. The feed chamber, together with the transition member 14, is formed as one unit; the unit is preformed, including half shells 18, 19. The outside part 16 of the transition member 14 is fixed to the bottom 9 of the feed chamber 6 coaxially with respect to the vertical axis of the cooling tube 2; in the feed chamber 6, an inside-tube section 13 is welded, and the inside-tube section 13 is protruded from the feed chamber 6 and aligned with the inside part 15 of the transition member 14. The thickness, the inside diameter, or the outside diameter of the half shells correspond respectively to those of the inside tube. The thickness, the inside diameter, or the outside diameter of the inside-tube section 13 correspond respectively to those of the inside tube. The thickness, the inside diameter, or the outside diameter of the half shells correspond respectively those of the outside tube 4, and the axial length of the half shell is made longer than the section of the inside tube protruded from the feed chamber 6.