Apply some fray removing liquid over the ends of the rip to prevent future fraying. You can purchase this repair liquid at most fabric or upholstery stores. Allow the liquid to dry for about one hour.
Fold the edges of the rip under about 1/8 to 1/4 inch, depending on how much excess fabric you can pull from the remainder of the upholstery. You want to place the weak threads as far away from the repair as possible.
Thread the needle with a double thickness of thread and knot both ends to secure the thread.
Sew the two sides of the tear together using a looped stitch. Pull the thread through both sides of the tear, then loop the thread over and pull it down through the same side of the tear, making a loop over the opened seam. Repeat the stitch until you have sewn the entire seam closed. Sew slightly beyond the end of the tear to strengthen the bond.
Tie a knot in the end of the thread to complete the repair.