A method for heat treating a synthetic quartz glass having a hydroxyl concentration with a maximum/minimum difference (ΔOH) of less than 350 ppm involves the steps of first heat treatment of holding at 1,150-1,060° C. for a time of 0.5-10 hours, cooling down to a second heat treatment temperature at a rate of −7° C./hr to −30° C./hr, second heat treatment of holding at 1,030-950° C. for a time of 5-20 hours, and annealing at a rate of −25° C./hr to −85° C./hr. Two stages of heat treatment ensures that the glass has a low birefringence.