The Black Cabal
The Black Cabal is an organization of magic-users, predominantly human, who once acted as the clandestine counterpart to the White Tower. Their existence has since become an open secret, and they have severed all ties to their former masters, due largely to an incident in Uldenor in which one of their members (The Kingslayer) assassinated King Ivan IV.
Their original mission was to act in direct opposition to the Laws of Magic proscribed by the White Tower, in very specific and limited engagements where the laws prevented white wizards from executing their own laws. Since the dissolution of ties with the Tower, they have rededicated themselves to finding and redeeming wayward magic-users before the White Tower can destroy them.
Name
The name "Black Cabal" is a reclaimed epithet created amongst the public by those who first theorized the group's existence; it was meant to convey feelings of betrayal and contempt for the White Tower's hypocrisy. Originally, the group had no official name, though within the White Tower, it was usually referred to as "The Contradiction" or "The Sixth Law", the latter more often referring to invocations of the group than to the group itself.
Today, the organization has officially adopted the name, deliberately accepting its negative connotation as an eternal reminder of the stain they bear--not the stigma of their magic, but the hypocrisy which made them necessary in the first place.