The Budget (No.2) Bill passed its second stage in the assembly, on 25 June 2012.
The bill's purpose is to allow the authorisation of money from the Consolidated Fund for 2012-13.
Finance Minister Sammy Wilson thanked the finance committee for consenting to accelerated passage for the bill.
Referring to a recent dispute between himself and the committee on this matter, the minister said it was "my powers of persuasion and nothing else" that won the committee around.
Mr Wilson conceded that the budget process "lacks transparency and is open to delay". He said that he had initiated a review into the process.
The minister outlined some of the main financial facts and figures, commenting that it was a technical bill but, "a crucial piece of legislation for our public services".
The deputy chairman of the finance committee, Dominic Bradley of the SDLP, said he would not dwell on the recent disagreement with the minister.
Mr Bradley said the committee supported the general principles of the bill, despite reservations over some matters, such as the use of the term "miscellaneous" as a budget heading.
The DUP's Paul Givan spoke about the difficulty of reading the budget document.
"In some ways you actually think it works as a cure for insomnia," he said.
Mr Givan said it was a good thing that the executive was not handing back money to Westminster and dismissed the disagreement with the minister as "a hullaballoo over a puff of smoke".
Mitchel McLaughlin of Sinn Fein said his party would support the bill.
He said the finance committee had been attempting to demystify the budget process.
The South Antrim MLA noted that other committees were unhappy with the time they had to consider the budgets of their own departments.
Ulster Unionist Leslie Cree said he disagreed with Mr Wilson's comment that 95% of the budget had already had been set in the 2011-15 budget document.
"Each budget year is a stand-alone year," he said.
Judith Cochrane said the Alliance Party would support the bill, but she raised a number of specific concerns, including funding for the voluntary sector, childcare and the cost of funding a divided society.
The motion was carried on an oral vote.