The bill is designed to expand nursery education for four year olds and to remove the statutory bar on grant maintained schools borrowing from the private sector.
Mr Squire also announced that the bill would not include measures on giving voluntary-aided schools a fast track to self-government.
'All institutions able to redeem vouchers will have to provide good quality nursery education - parents will be certain of that. All institutions will work towards the same goals for children, focusing on literacy and numeracy. And all institutions will be inspected on the same basis.
'Parents know what is best for their child, and with a voucher they will be able to exercise that choice - choosing between the state, private and voluntary sectors.'
Commenting on the part of the bill on GM borrowing, Mr Squire said:
'Devolving power to institutions has been a central feature of this government's education reforms. We have given local management to all state schools, and we have also given schools the option of becoming fully self-governing, by becoming grant-maintained.
'Control and management of resources - including a school's land and buildings - are important aspects of self-government.
The bill therefore provides for GM schools to borrow commercially in order to finance capital spending.
'This new facility for GM schools would bring them into line with colleges and universities. It would allow increased investment in GM schools. And it should help schools to benefit from the private finance initiative.
'It is a positive and practical measure. It has the broad support of the GM schools and others who responded to our consultation. And it is a logical extension of the principle of self-government, now that GM schools have demonstrated their ability to manage resources effectively.'
Mr Squire also confirmed that the bill would not include measures to create a fast track to self-government for voluntary aided schools. He said:
'We received almost 2,000 responses to our consultation paper and we have taken very careful note of what they said. Two messages came over very clearly.
'Firstly, that the churches and their schools do not want special treatment, but feel that the same procedural arrangements should apply to them as apply to other schools.
'Secondly, that there is support for maintaining the existing arrangements for applying for GM status, and particularly for the role of parents in this process.
'In the light of these views, we havedecided not to amend the legislation governing the acquisition of GM status for the time being. But we shall continue to build on the success of the GM programme.
'We remain fully committed to extending the benefits of self-government to all schools. We are examining a range of longer-term options and the many responses to our consultation paper will help to inform our continuing work'.