PURPOSE: Undrawn polyester yarns resulting from high-speed spinning are heat treated in a dry or wet heat atmosphere kept in a certain range, then drawn to produce the titled fiber dyeable by normal pressure operation with high fastness as well as heat resistance and strength.

CONSTITUTION: The polymer is melt extruded from the spinning head 2 at a speed exceeding 4,000m/min, passed through the tubular heating zone 3, the fluid sucker 4, the finishing oil applicator 5 and the yarn collector 6, then wound up around a roll 7 to prepare undrawn yarns. Then, the undrawn yarn is passed through the yarn way 18 that is adjusted in temperature to 240W300°C by the heater 14 set in the heat treatment unit 17 to effect dry heat treatment, then drawn between the feed rolls 19 and the drawing rolls 20 or the yarn is treated with wet heat at 180W300°C by sending saturated steam from boiler 9 to the steam heater 11 and opening the valve 13 then drawn at 1.05W2.0 draw ratio to give the objective fiber.