PURPOSE: To enable a bonding wire to be enhanced in breaking strength and mechanical properties so as to be lessened in physical property variation.

CONSTITUTION: A fine wire 5a (6a) of gold or gold alloy is annealed in an atmosphere of either inner gas or reducing gas. For instance, an annealing device 1 is composed of a tubular electrical oven 2, a gas feed device 3, a control device 4, and a bonding spool 7 which sends the gold wire 5a (or gold alloy fine wire 6a) into the tubular electrical oven 2 feeding it, and a bonding spool 8 wound with the annealed gold fine wire 5b (or gold alloy fine wire 6b) at a prescribed speed. Ar gas, N2 gas, CO2 gas or the like is used as inert gas, N2+10% of H2 or N2-I-10% of Hz is used as reducing gas, and an annealing process is carried out in a temperature range of 300-600°C.