The first time I encountered the intimidating presence of the one-time sergeant major in the King's African Rifles was 26 years ago at a military ceremony in West Nile Province, his home tribal district.
Amin listened to bagpipe music and named his sons after Scots clans
We landed on an old British colonial airstrip in one of his Hercules transports, normally used to import scarce luxury goods for the Ugandan dictator and his henchmen.
It was a scorching day but Amin was wearing his field marshal's kit with its specially lengthened tunic - reaching almost to his knees - to accommodate all the medals he had awarded himself.
Glinting in the sun was his Victoria Cross as self-proclaimed Conqueror of the British Empire.
He was an obvious bully but capable of menacing charm. He was by no means stupid though he devoted his energy to preserving his own tyranny as well as liquidating his enemies and those who possessed something he wanted, like an attractive wife.
Grouped around him were his hardcore toadies, headed by a seedy expatriate known universally as Major Bob.
For hours Amin reviewed a military march-past, one of his favourite pastimes.
By early 1979 his grip on power was slipping. A comically absurd series of attacks on Tanzanian territory by his incompetent and often drunk soldiers finally provoked President Julius Nyerere.
The Tanzanian leader mobilised an armoured column and after several months it was closing in on the Ugandan capital, Kampala.
Colonel Muammar Gaddafi of Libya sent his own intervention force to try to bolster Amin but they too proved almost useless and the Ugandan army retreated towards Jinja.
We were the first foreign correspondents to reach abandoned Kampala and, through crowds dancing in the street, we immediately went to the headquarters of his secret police, the State Research Bureau, SRB.
Below ground level the power had failed. We stumbled down the stairs of the empty building into a charnel house. The floor was awash with blood, the bodies of the SRB's last victims lying in the darkness in their concrete dungeons.
Upstairs, the electricity was working. In one vast room we found the SRB's abandoned wiretapping operation still functioning.
Amin refused to accept responsibility for years of brutality
Neat rows of Akai tape recorders were patched into Kampala's phone grid - the spools rotating, pencils and pads on the desks for the note-takers who had fled.
Who knows how many phone calls the secret police thugs had intercepted over the years with fatal results?
In another room stuffed with files marked Top Secret, I found one detailing the surveillance of my BBC colleague Philip Short who had been expelled by Amin.
Then we headed for Amin's living quarters in Nile Mansions. The priority was to search the refrigerators because of persistent reports that he sometimes kept the heads of his victims in the freezer.
With relief, we found no evidence to back this up.
Within a few weeks, Idi Amin escaped from Uganda, probably with the help of Colonel Gaddafi.
Idi Amin's house in Jeddah where he lived with one of his wives and 25 of his children
Tracked down to Jeddah
A year later, in partnership with cameraman Mohammed Amin of Visnews in Nairobi, I mounted a search for the fugitive strongman.
Eventually we located him in the Saudi city of Jeddah.
The Saudis had been staunch allies because Idi was a Muslim convert who ordered mosques built across Uganda when he was in power.
After weeks of negotiation through an intermediary we fixed a meeting at his hideaway in Jeddah.
He stipulated the interview had to be done clandestinely without the knowledge of the Saudi authorities.
We rang the bell and the front door was opened by several nervous Saudi government bodyguards.
They would not admit us. Then Idi appeared behind them and loudly told them: "These visitors are my guests. You all know I am living here at the invitation of the King. Do not interfere."
Looking stressed but cowed by the mention of the monarchy, the Saudi secret police retreated to the kitchen.
Amin beckoned us to the lounge reverberating to bagpipe music - he was playing a recording of the Edinburgh Tattoo at maximum volume.
Idi Amin talking to Brian Barron at the exiled dictator's home in Jeddah
After introducing us to two of his sons, both with Scottish clans as their Christian names, Amin gave me a 45 minute interview.
He was relaxed and clearly homesick, promising he would regain control in Uganda.
He rejected any responsibility for the years of brutality, for the murder of his opponents, for the scenes of horror we had witnessed at the SRB headquarters.
All had been fabricated by his enemies, he insisted.
What he told us that evening in 1980 was a lie from beginning to end.
Idi Amin was the most flamboyant of a group of African dictators I covered during that turbulent period.
Emperor Bokassa, another army sergeant gone wrong, in Central Africa; the mad, bad General Siad Barre in Somalia; the psychopathic Sergeant Doe ruling Liberia.
Despite Amin's crimes against humanity, he escaped justice for one reason only: the Saudi authorities shielded one of the monsters of our time.
Brian Barron is now BBC South Europe correspondent based in Rome.