The Black Ajah is the term generally used for those Aes Sedai who are Darkfriends. Their existence is often denied by the White Tower, but they do exist. It is not a true Ajah, and Black Ajah sisters also belong to another of the White Tower's Ajahs. It is thought that they have been freed from the Three Oaths.
The Supreme Council, which consists of thirteen sisters, is in charge of the Black Ajah, but they are also required to answer to the Forsaken as required. Alviarin is the current head of the Black Ajah, presumably at the head of the Council; her predecessor, Jarna Malari, was killed by Ishamael for her bungling. They are organized in groups of three called "hearts"; most sisters know only one other who is outside her heart, but some know more.