I agree with @Humblefish look at you light first, the PH. Cyanobacteria is just that, a bacteria. The best way of getting rid of is starving it. You can do that by dropping the nutrients (Po4's No3's) The reason I ask about PH is the cyano seems to feed off of CO2 meaning is spread more with low PH values.
The easiest what to get it out of your system is a cyano remover. I have used the red slime remover and it works will. I have had cyano outbreaks over the last year and I am going to try the Zeovit cayno remover. It seems the you can use the remover and then use the remover as a maintenance dose.