Slayer frontman Tom Araya says politics within one band are preventing more Big 4 thrash shows.
And he suggests disagreements had already appeared before Metallica, Slayer, Megadeth and Anthrax played their last concert together.
Fans of the genre were delighted when the acts teamed up for a series of appearances in 2010 and 2011, immortalised in a live DVD release which topped sales charts across the world.
But there's been no more action since then – and Araya believes it's likely to remain that way.
He tells Gazette.net: "I don't want to day politics is preventing that. It's not the politics between bands – it's the politics of character in one particular band.
"We had an issue that came up on the New York show which really freaked everybody out. The New York show happened; I think that was the last time we did the Big 4.
"I think another Big 4 show might not happen – they could prove me wrong."
But if the opportunity presents itself Araya vows Slayer will be there. "Even though it was called the 'Big 4' it was done through Metallica. It was Metallica's blessing that allowed those shows to happen.
"If they want to do a couple more shows, I think that would be great. If we were to sit down and communicate with them, that's what I'd tell them."