I have a Septic system and have been told not to use a Bleach. So what kind of a whitener can be safely used in a Septic System?

Bleach is actually fine to use with a septic system, as long as you don't over use it. If you do 1 to 2 loads a week with bleach it shouldn't cause any major problem with your septic system, provided your septic is in good shape. The problem with bleach in a septic system is that it kills the helpful bacteria that break down the waste. Only doing a couple loads a week with bleach won't kill enough bacteria in your system to cause a problem, I've been doing it for years with no ill effects.

I agree with lilpoppa, bleach used for normal laundry is fine. There are, however, alternatives to bleach if you care to try them. Natural Bleach Alternatives | Passionate Homemaking