A novel high tensile strength semi-absorbable composite suture (10) with minimized non-absorbable mass. The suture has a core (60) made from a bioabsorbable polymer (70). The core is covered by a braided sheath (20). The braided sheath is made from a nonabsorbable yarn (30) and a bioabsorbable yarn (35). The bioabsorbable yarn is made from a least one filament of a bioabsorbable polymer. The nonabsorbable yarn is made from at least one filament of ultra high molecular weight polyethylene.