After the chlorine level has come down below 5 ppm, add an algaecide and brush the pool again. Check and rebalance the pool water if necessary. Filter, Filter, Filter. For black algae, the brushing part is very important. You must tear through the protective layers so the chemicals can destroy the plant from the inside out.
Pumice stones work well to knock off the heads of black algae.
Rubbing the spots on the walls with a trichlor tablet or stick can also be effective to knock off the heads and get trichlor directly to the roots. Follow up with a dose of copper algaecide , or high strength polymers. Simazine, an herbicide, was a very effective black algae treatment, but is no longer available in America. If algae has been an ongoing problem in your pool for several years, you may do well to drain the pool. Many years of algae builds up dead algae cells and lots of other solids in the water that contribute to its rejuvenation.