"I will be their voice': Lidia Thorpe to pursue 'Blak' sovereignty as an independent

And the when, just to wake everyone up, turned out to be the first parliamentary day of the year.

"On stolen land, of course ..." the new independent senator began.

With an overwhelming sense of inevitability, and allowing no media questions to be asked, Senator Lidia Thorpe ripped the cord, and left the Greens to champion black sovereignty as an independent.

To do it "fully".

"Now, I will be able to speak freely, on all issues, from a sovereign perspective, without being constrained by portfolios and agreed party positions," she said.

"There is a black sovereign movement out there that no-one wants to listen to, so I will be their voice."

The defector now deserts Victorian Greens voters and members.

She was the Greens' First Nations spokesperson, but the Greens have struggled with having different views, particularly on the proposed Indigenous Voice to Parliament.

The way is now clear for the minor party to announce Voice support, a position most Greens voters have been polled as backing.

The enabling legislation for the referendum should now pass.

Senator Thorpe is not yet in the "No" camp, but she may as well be as she is insisting - despite plans barrelling along for a referendum this year - on a First Nations' Treaty before a Voice. She also has been demanding a guarantee First Nations sovereignty is not ceded through a Voice. Eminent constitutional experts attached to the referendum working group have not satisfied her.

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Greens leader Adam Bandt was at pains to point out her departure was her decision, she is a "fighter" who could return if she wanted. And she could have had a different position on the Voice under the Greens' constitution.

"She's obviously decided to adopt a different course," Mr Bandt told reporters.

Has this been on cards? You betcha. Senator Thorpe's fit in the Greens has been questioned by people in and outside the Greens.

Most notably last October when it was discovered she had an undisclosed relationship with a bikie while sitting on a committee looking into related matters. She was stripped from her deputy Senate role.

But she does have a substantial constituency for her firebrand advocacy for First Nations people.

"My focus now is to grow and ... amplify the black sovereign movement in this country!" she detailed.

Asked twice on Monday if he believed the senator had acted with "propriety" during her time with the Greens, Mr Bandt just said she left with respect.

The senator's shift changes things in the make up of the Senate. With a number now carved off the Greens' bloc, and if the Coalition opposes legislation, the Albanese government will need the Greens plus two crossbenchers to get up to the magic number of 39.

Senator Thorpe said she would vote with the Greens on climate, but made no assurances in any other field.

Mr Bandt is hoping there will be "large" overlap with her in other policy areas. Other than that she will have to "speak for herself". The job description itself for an independent.

As for the Senate crossbench, she's been warmly welcomed by Jacqui Lambie, who said becoming a crossbencher "takes guts".

"Love to see it," she tweeted.