Mix the bleach solution for cleaning the mold growth off the wall. A mixture of 1/4 cup to 1/2 cup bleach diluted in 1 gallon of water is ideal for this purpose. Depending on the amount of powdery mold growth on your basement walls, you may need to mix more than 1 gallon of the solution.
Remove the mold growth using the bleach solution and an abrasive scrubber. Keep scrubbing until no powdery mold colonies remain, though take care to not damage the walls with the force of your scrubbing. Allow the wall to dry thoroughly after scrubbing.
Eliminate the source of moisture that caused the mold to grow on your basement walls in the first place. No matter where mold grows in the home, an integral step in cleaning it up is to eliminate the source of excess moisture that molds need in order to survive. Check floor drains, plumbing attachments, appliances, ceilings and walls for any leaks, and have the leaks repaired at once. This will help ensure that more mold colonies do not form on your basement walls in the future.