The trade union royal commission's spotlight turned back to alleged corruption in the national construction union a day after commissioner Dyson Heydon dismissed the union's call that he stand aside on the grounds of alleged bias.

In a 67-page judgment explaining his reasons for rejecting an application from unions that he disqualify himself from the inquiry, Mr Heydon said the Sir Garfield Barwick Address which he had agreed to attend as a keynote speaker was a "legal event" in nature. The event was organised by a lawyers branch of the Liberal Party.

The retired High Court judge ruled on Monday that the union complaints of bias were not established and "must be dismissed".

On Tuesday, Mr Heydon was back in the commissioner's chair to hear allegations of blackmail and standover tactics against against the Construction Forestry Mining and Energy Union's Canberra branch.

During recent Canberra hearings, a builder told the royal commission he had lost job contracts after he refused to pay the CFMEU bribes.

Troy Armstrong, the owner of Claw Constructions in the ACT alleged that CFMEU ACT organiser Tony Vitler warned him in 2012 that he would not get work if he refused to sign an enterprise agreement with the union, or make donations.

Mr Armstrong alleged that Mr Vitler said the union could guarantee him work when the pair met at the McDonalds in Fyshwick.

But in sworn evidence to the royal commission on Tuesday, Mr Vitler denied trying to bribe Mr Armstrong during their meeting at the Fyshwick McDonalds.

"I did ask him which jobs the company was on. I did encourage him to sign the EBA. I did not make a statement that I could guarantee his company work," Mr Vitler said.

"I did speak to Mr Armstrong about membership. I deny making any statement to Mr Armstrong about donations. I did not say anything that would make Mr Armstrong believe I was leaning towards a bribe."

After giving evidence to the royal commission in July, former CFMEU ACT official Halafihi "Fihi" Kivalu was arrested and charged with blackmail in July. He was released on bail and has pleaded not guilty.

Former Canberra Raiders rugby league player, John Lomax, who became a CFMEU official, was later arrested and charged with one count of blackmail after allegedly pressuring building contractors to sign workplace agreements. The arrest followed a royal commission investigation.

The hearing continues.