Lawyer S K Mangalam filed the petition on behalf of Gyanendra Singh Gyanoo, Neeraj Singh Babloo, Ravindra Rai and Rahul Sharma.
Mangalam told reporters that the termination has been challenged as "unlawful and unconstitutional".
Speaker Uday Narayan Chaudhary had on Saturday last disqualified the four rebel JD(U) Legislators as members of the Assembly on the charge of working against the party during the recent bypolls to two Rajya Sabha seats in the state.
The four have not been given status of ex-MLA in the Speaker's ruling thus depriving them of all benefits in that capacity.
The MLAs were charged with working as proposers and polling agents of rebel candidates Anil Sharma, a real estate baron and expelled JD(U) leader Sabir Ali in the bypolls.
After RJD and Congress had extended support, the two official JD(U) candidates - diplomat-turned-politician Pawan Verma and Gulam Rasool Balyawi - had won from the two seats defeating the rebels.
In the petition, the MLAs have alleged that the Speaker's order violated 10th schedule of the Constitution, Gyanoo said.

"The provisions under 10th schedule is applicable within the Legislative House and not outside. The voting for two Rajya Sabha seats had taken place outside the House," Gyanoo, once a close confidante of former Chief Minister Nitish Kumar, said.
It has been said that by becoming proposers of the unofficial candidates "we violated law under 10th schedule.

But, there were over a dozen proposers from JD(U) so why only eight of us have been chosen for action?" he said, describing the action as "vindictive".
"Not recognising us as even ex-MLA is blatant violation of laws," he said.
Besides terminating the membership of the four, the Speaker has called four other JD(U) MLAs facing similar charges on November 22. They are--Poonam Devi, Ajit Kumar, Suresh Chanchal and Raju Kumar Singh.

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