First you must know that the red slime algae often seen is really a bacteria and it comes in several colors. Black, dark purple and super bright green are also colors with red being the most common. It is found in tanks with poor water quality, poor lighting, and/or poor circulation. Since any or all of these conditions can cause this soft, colorful coating to grow in your tank, you may have to correct more than one problem. The biggest reason is usually circulation. Re-direct your power heads or add another because cyano bacteria hates moving water.
If adjusting circulation, changing to new bulbs and doing water changes fail, then do the following. Siphon out as much cyano bacteria as possible. Add new, clean saltwater to replace what was siphoned out. Then because it is a bacteria, one method of removing it is by adding erythromycin. This is a strong antibiotic and must be used sparingly. One capsule or pill (200 mg) is enough to clear up a 55 gallon with a small outbreak. A 100 gallon tank with a very heavy amount of slime algae may need 4 capsules. Use your judgment. Open capsules and mix with saltwater because the capsule itself will not dissolve. Crush pills and mix with saltwater. (Do not add the recommended amount as per package instructions; it will kill all the good bacteria in your tank too.)Turn off ozone, protein skimmer air, and remove carbon and other absorbents, etc. Add erythromycin after the lights are off (or just turn them off). All of the algae (bacteria) should be dead by morning. If not, repeat the next night - again leave the lights off for the entire day. When it is gone, turn on the skimmer, do a 33-50% water change then add an alkalinity booster. Fresh carbon can be used for 3 days if you don't have a skimmer. Keep your particle filter clean - everyday or 2.
I have used this method with much success