With the high price of shoes, it often makes more sense to fix a shoe than to throw it out. If your heel strap is broken, it's not the end of the world. Most likely, you'll be able to fix it and make it almost as good as new, particularly if the leather, cloth or plastic of the heel strap hasn't torn significantly. If you're careful, you can make a repair that will give your shoe a second life.
Clean the strap by brushing any dust or dirt off with a dry cloth, since the material must be clean and dry to glue it properly. Trim off any stray threads or jagged pieces.
Apply several small drops of glue to each part of the strap that you want to glue. Allow the glue to cure for two minutes before bringing the heel strap parts together.
Bring the two parts together and press together gently. Place in a clamp and tighten just enough to hold the pieces in place. Place the clamped shoe on a piece of newspaper on a flat area.
Let the glue dry for at least 24 hours. Test before using by pulling on the strap pieces to make sure the hold is tight. Clean up any extra glue on the edges by putting acetone or paint thinner on a cotton ball and rubbing gently until the extra glue balls up and brushes off.