A novel process is disclosed for extruding an absorbable glycolide/lactide block copolymer into multifilament suture fibers. The block copolymer preferably consists of about 50/50 mole % of Glycolide/Lactide in the center segment and the overall composition of the copolymer is about 90/10 mole % Glycolide/Lactide. The novel extrusion process comprises the steps of maintaining the temperatures of at least two, preferably three or more, of the extrusion zones in the range of about 5-50° C. below the polymer melting point. The multifilament suture made with the invention process from the segmented, glycolide-rich, poly(glycolide-co-lactide) copolymers of A-B-A type, where the B-segment is an amorphous prepolymer of glycolide and lactide in the molar ratio of about 50/50 glycolide/lactide, exhibit exceptionally high breaking strength retention (BSR) at 42 days post-implantation.