A green investment bank: what's not to like? Banks might not be flavour of the month, but if they invest in the right things, that's good. And there are any number of projects that would benefit the environment, yet struggle to raise backing from conventional financial institutions. Many environmental campaigners had been calling for a green bank for years. So this is an initiative we can welcome, right?

Well, politics is a funny world. Even when you think they've listened, and the words they use are just the ones you'd have chosen yourself, it's always best to check the small print. And with the coalition's version of a green investment bank, testing each word is an education in sophistry.

Let's start with the word "bank". We all know what a bank is: it borrows and lends money (and may or may not also pay its senior executives millions in bonuses for being clever enough to manage this complex transaction). Except that it's not at all clear that this bank can borrow or lend. Without these powers, it would be a fund – that is, a pot of money that, once used up, is gone forever. Maybe something still to be welcomed, but not a bank that can recycle the money it receives and so invest it again and again, producing far more benefit over the long term.

How about the word "green"? The way businesses sometimes stick "green" on the front of things they want to flog is definitely in the "don't get me started" category. But here, surely, the green investment bank will invest in new green projects: reducing energy consumption and waste, supporting clean energy generation, or backing "lean" technologies that use less raw materials in manufacturing. Projects that may be just on the edge of being viable, say, or have a risk element that puts off traditional investors. Projects a bank that offers good interest rates on loans, and understands the sector, could really benefit from.

But there are signs the coalition is considering allowing its green investment bank to fund nuclear power. Even if you think nuclear could help reduce greenhouse gas emissions, it's still a bit rich to call it "green", given the huge question of waste. And it certainly isn't a new technology. Plus, the huge costs of a nuclear power station would quickly eat up the funds available in the Bank for other projects. Any commercial pay-back for nuclear is likely to take decades to emerge. And crucially, using the bank in this way would undermine the coalition's pledge not to use public money to subsidise nuclear.

Fortunately, I'm not alone in having concerns about the way the bank might develop. And to be fair to the coalition, they still have the chance to confirm that it will have the power to lend and borrow, and sufficient capitalisation to make a significant impact on the backlog of important pro-environment projects. They can also confirm that it will not be funding nuclear projects.

But perhaps what we need most is the right board for this new bank. Not the kind of board we've seen at some other banks I could name – presiding over mismanagement and the creation of huge toxic debts and ignoring their vital role in society, all the while trousering unjustified salaries and bonuses.

We want a board of people who understand finance, but also industry, society and the environment. Who are on the board to ensure it invests in the right ways: not to maximise profits, but to meet its environmental and social potential and responsibilities and so generate a greater return for our country than profits alone can ever do.

Get that right, and the bank could be one that all of us can be proud of – no matter what it's called.

• Caroline Lucas is the leader of the Green party of England and Wales and the country's first Green member of parliament