Gordon Brown has proposed the Scottish Parliament get new powers over income tax as part of a plan to create a "partnership of equals" between Scotland and the rest of the United Kingdom.
The former prime minister said the six changes he was proposing would transform the "unitary and centralised" system in the UK.
As part of that, he suggested that the Scottish Parliament should raise about 40% of the cash it spends and said giving Holyrood more powers over income tax was the best way to achieve this.
Mr Brown has submitted his proposals to Labour's devolution commission, which will shortly put forward plans to boost devolution in the event of a No vote in September's Scottish independence referendum.
In a speech in Glasgow, the former Labour leader said: "We need to build the future of the relationship between Scotland, England and the rest of the United Kingdom.
"I believe there are six constitutional changes we have got to make for a better relationship between Scotland and the rest of the United Kingdom, to turn what I would call a unitary and centralised state of the past into a partnership of equals and one where there is power-sharing
across the United Kingdom."
Sir Menzies said politicians should take advantage of the public appetite and momentum for more powers created by the independence referendum to act swiftly towards further devolution.
As part of his submission to Labour's devolution commission, Mr Brown argued more tax-raising powers should come north.
Scotland is already due to get new powers over income tax from April 2016, when the UK Treasury will deduct 10p from standard and upper rates of income tax in Scotland and give MSPs the power to decide how to raise cash.
Mr Brown went further than this, though, saying: "The first 5p of income tax should be decided by the UK Government, the next 15p by the Scottish Government.
"I believe that is a fair way of raising 40% of the revenue of the Scottish Parliament in Scotland."
This, he argued, would make Holyrood ministers "accountable to the people of Scotland for the way that money is spent", adding: "They will have to answer at elections, which they don't have to do at the moment, for tax decisions that they make."
He also appeared to indicate the Scottish Parliament could get some power to alter the top rate of income tax, saying that "if the fairness of the Scottish Parliament was being undermined by unfairness elsewhere then there should be power to do something about it".