Polyester yarn is made by melt spinning the polyester filaments which are then cooled at least to solidification and heated by counterflow with prestretching to a crystallinity in excess of 24%. The prestretched filaments are gathered and stretched to after-stretching at a temperature of 80.degree. C. to 250.degree. C. to a final titer of 1.0 dtex to 7.5 dtex with a stretching ratio of 1:1.5 to 1:1.15. The yarn is then wound up at a rate of 5000 to 8000 m/min.