Set the trimmer on a flat workbench. Remove the four hex screws that hold the starter recoil to the end of the engine; slide the starter recoil off the engine.
Heat each end of the new rope with a lighter so the rope will not fray. Remove the old rope by pulling on the knot at each end and slide the old rope out. Turn the drum counterclockwise until it tightens against the spring; hold the drum in place with your thumb. Slide the new rope through the housing and through the drum; tie a knot in the end to hold the rope in place.
Slide the other end of the rope through the handle and tie another knot in that end; release your thumb from the drum and allow the rope to wind into the recoil. Place the starter recoil over top of the engine, reinstall the four hex bolts and tighten them.