New South Wales senator Lee Rhiannon could be censured or even expelled from the Greens parliamentary party room in coming days, following a bitter split from her colleagues over the Government's school funding legislation.

Key points: Greens senators have the right to exercise conscience vote but have to inform their colleagues

Greens senators have the right to exercise conscience vote but have to inform their colleagues Lee Rhiannon is accused of breaching party rules

Lee Rhiannon is accused of breaching party rules Senator Rhiannon authorised leaflets that said Government's plan would "rob" public schools of funds

All nine of Senator Rhiannon's colleagues have signed a letter of complaint, accusing her of breaching their trust and party rules.

The ABC understands the Greens National Council has decided it is a matter for the party room to resolve, and that is likely to happen this week.

The Greens voted against the Government's $23.5 billion school funding plan, dubbed Gonski 2.0, despite securing almost all of the concessions it had requested.

Greens Leader Richard Di Natale said he was still negotiating with the Government in good faith, when it became apparent on Wednesday it had secured enough support from other crossbench senators.

The Greens eventually opposed the legislation because it gave around $50 million in transitional funding to the Catholic education system.

But the party had also been under enormous pressure from the Australian Education Union, and it struggled to come to a final consensus on any deal with the Government.

Greens senators have the right to exercise a conscience vote, but they must inform their colleagues once they have decided to do so.

Senator Rhiannon is accused of breaching party rules by deciding about six weeks ago she would campaign and vote against the legislation, without telling her colleagues.

The issue came to a head when a leaflet, authorised by Senator Rhiannon, was distributed in Sydney, while Senator Di Natale and the Greens education spokeswoman Sarah Hanson Young were still negotiating with the Government for billions of dollars in extra funding.

The leaflet said the Government's plan would "rob" public schools of funds.

Senator Rhiannon has used a Facebook post to reject the idea she had any impact on the negotiations with the Government.

"At all times my actions on education have been faithful to the Greens policy and process," she wrote.

"It was the Turnbull Government's decision to do a deal with the crossbench senators that killed off negotiations with the Greens."

She described the leaflet as a "good initiative of local Greens groups".

Even if Senator Rhiannon was expelled from the party room she would not be kicked out of the Greens altogether, but would sit independently on the Senate crossbench.