Until 1992 the Ulster Defence Association was a legal organisation in Northern Ireland. So, despite the fact it was responsible for some of the most appalling violence of the Troubles, it had no need for a political "wing".
It was proscribed after members of its south Belfast brigade killed five Catholic men - ranging in age from a 15-year-old to a pensioner - in Graham's bookmakers on the Ormeau Road in February that year.
When it became illegal to belong to the UDA, the organisation had to find another persona with which to promote its political views.
The UDP had already been in existence for some years, having changed its name from the Ulster Loyalist Democratic Party (ULDP) in the early 1990s. Its main spokesman was Mr Gary McMichael, son of the UDA leader, John McMichael who was killed by an IRA bomb in December, 1987. The organisation was, in political terms, inconsequential.
Gary McMichael had, at his father's insistence, been directed away from the violent side of loyalism, and has had no connections with the "military" side. With the approach of the republican and then loyalist ceasefires in 1994, the UDP came into its own and Mr McMichael Jnr emerged as the surprisingly articulate and moderate new face of the UDA. His close political associate, Davy Adams, is a similarly moderate and non-military figure. The same, however, cannot be said for some of the others around this pair.
John White, the party's number three spokesman, who appears regularly on television as part of UDP delegations, has a self-confessed paramilitary background.
After an attack of conscience, he walked into a police station to admit two of the most shocking killings of the Troubles - the murders of the SDLP's Senator Paddy Wilson and his companion, Ms Irene Andrews, in June 1973.
Mr White was subsequently sentenced to life imprisonment for his part in the murders.
Paradoxically for an organisation with such a record of sectarian killing, the UDA and the other, better organised, loyalist organisation - the Ulster Volunteer Force (UVF) - both have quite moderate political policies.
The UDA followed the UVF in the mid-1970s by adopting powersharing and a bill of rights as policies. The UDA leaders, Andy Tyrie and Glenn Barr, put forward a number of quite progressive papers under the aegis of a group called the New Ulster Political Research Group (NUPRG) in the late 1970s.
John McMichael took up the political lead again in the mid1980s with the launch of a new policy document called Common Sense, again advocating power sharing. Mr McMichael, who was simultaneously head of the military side of the organisation, stood in one general election but received a derisory vote. He remained as the UDA spokesman but quietly shelved his political ambitions.
After his murder, the UDA fell into a period of internal turmoil. In the early 1990s it resurfaced, with an articulate and intelligent spokesman, Ray Smallwoods. He had served a 15-year sentence for attempting to murder Bernadette McAliskey and her husband, Michael, at their home in Coalisland in 1980. The McAliskeys were repeatedly shot in front of their three young children and survived only because of the intervention of a British army patrol.
Mr Smallwoods, with the support of some key members of the UDA's seven "Inner Council" members, helped steer the organisation towards a ceasefire, and encouraged and assisted in promoting Gary McMichael as the acceptable face of the UDA.
Mr Smallwoods was within sight of achieving his aim of putting the UDA on a peaceful and legitimate footing when he was shot dead by the IRA.
Mr Smallwoods' murder, and the subsequent purging of a number of key moderate figures in the UDA - most importantly the former east Antrim commander - allowed the slow drift back towards violence and to the killings of the past month, leading towards yesterday's departure of the UDP from the talks.