It is even more unusual when the business in question is a clearing bank, that very model of probity, dependability and continuity. And it is virtually unheard of when the chief executive in question is giving up a salary of pounds 675,000, and the lifestyle that goes with it, without a new job to step into.
And yet that is what Martin Taylor, the chief executive of Barclays Bank, did yesterday morning, to the amazement of the City, the banking industry and, most of all, his 61,000 staff.
The drama began to unfold last Monday morning. Mr Taylor, who had been with the bank since 1993, left his regency terraced home in Blackheath, south-east London, with something important on his mind.
He is a man with a reputation for being decisive. By the time he arrived at Barclays' offices in the heart of the City, he had decided to tell his closest colleagues of his intention to leave.
By noon that day, he had made his intentions known to about 10 senior executives within the bank. Sir Andrew Large, the deputy chairman, was away on business in Kuala Lumpur, so the job of handling the succession crisis was passed to Sir Peter Middleton.
A former mandarin and a board member of Barclays for seven years, Sir Peter is an old hand at dealing with controversial departures. As permanent secretary at the Treasury, he dealt with Nigel Lawson's resignation as chancellor.
Sir Peter telephoned the bank's most senior non-executive director, Sir Nigel Mobbs, the boss of the property group Slough Estates.
Sir Nigel met Mr Taylor the following day to discuss his resignation and, it is thought, to test out whether the chief executive could be persuaded to stay.
When it became apparent that Mr Taylor's mind was made up, a board meeting was convened for Thursday evening, immediately after Sir Andrew had landed back at Heathrow from the Far East, to accept the resignation and agree severance terms.
So to the announcement. The official, authorised version of Mr Taylor's departure from one of the biggest jobs in British business at the age of just 46, is that he had completed his task at Barclays. After five years in the top job, it was time to move on and hand the baton to a new management team.
From the chairman down the line never faltered yesterday. And, in case any members of the bank's staff were tempted to give a different account, there was a large notice in the marble-tiled lobby yesterday sternly instructing them not to speak to the press.
The official mantra, repeated all day yesterday, was as follows. There had been no boardroom bust-up. Mr Taylor's decision to leave was entirely his own. There was no dispute over the bank's strategy and there was quite definitely no black hole lurking in its accounts.
The problem is that no one believes Barclays, not even the City spin doctors brought in to try to keep a lid on the affair. What can be said with certainty is that Mr Taylor's departure is not connected either to ill health or to a "Ron Davies factor".
Beyond that, the City is awash with speculation. The commonly held assumption is that Mr Taylor had a seismic and irreconcilable difference of opinion with the rest of the board about where the bank should be heading.
As one pin-striped, red-braced American executive at Barclays observed yesterday: "When someone like Taylor leaves like this, it is either a disagreement of policy or he has been asked to leave."
Mr Taylor, bound by confidentiality, legal restrictions and a big fat pay-off, would give nothing away yesterday, but he did volunteer one telling comment to the London Evening Standard newspaper: "This has been coming for a while. Crucially, it is about my ability to get things done." Those do not sound like the words of a man who has come to a natural hiatus in his career and has decided to part company with his employer amicably.
The things that Mr Taylor wanted to "get done" are well known. Barclays has 21 million account holders, 20 per cent of both the personal and small business market, 2,000 branches and, in Barclaycard, the country's biggest credit card. But for all its size, Barclays has become a minnow in world banking terms.
The eagle that is the bank's symbol first spread its wings in 1736 when James Barclay joined with a family goldsmith and banking group under the sign of a black spread eagle.
By the late 19th century, it had grown to become Britain's second biggest bank after the Midland and by the late Fifties it had surpassed the Midland. Barclays' prime position as Britain's biggest bank was one of the reasons why it was targeted so unrelentingly throughout the Seventies by anti- apartheid groups protesting at its investments in South Africa.
But in the last decade, the bank has lost ground. In terms of market capitalisation, at pounds 22bn, it is half the value of Lloyds-TSB and HSBC, the owners of Midland. On an international scale, it pales by comparison with some of Wall Street's bulge bracket banks like Citigroup.
Mr Taylor's answer was to engineer a takeover of another financial institution or a merger of equals. For a long time NatWest was in Barclays' sights until it became obvious that, despite Mr Taylor's closeness to Labour, such a concentration of high-street banking would not be permissible.
But Mr Taylor, by his own account, also discussed the possibility of a merger with Standard Chartered bank over dinner with its chief executive, Malcolm Williamson, in February this year, although the two men cannot agree on who popped the question first.
The latest speculation is that Barclays has approached the mortgage bank Halifax about a marriage. Six months ago, Barclays would have been able to eat Halifax for breakfast with its superior market capitalisation of pounds 30bn. Now, however, it would be a merger of equals, Barclays shares having fallen by 30 per cent from their peak this year.
When Mr Taylor arrived five years ago in the aftershock of recession, reckless bad lending and Barclays' first ever loss, it still had pretensions to be an investment bank on a world scale. However, it has since reined in its ambitions. Along with NatWest, Barclays has been forced to beat an ignominious retreat from investment banking, taking a pounds 688m loss on the sale of BZW to Credit Suisse First Boston.
Unfortunately, the investment banking business it did retain, renamed Barclays Capital, has scarcely fared any better. Barclays was hit hardest among all British banks by this year's financial collapse in world markets. It lost pounds 250m through the Russian crisis and was also caught up in the collapse of the hedge fund Long Term Capital Management, emerging as one of the banks that had contributed to its $3.5m (pounds 2.1m) bail-out with a $300m investment.
All this has taken its toll on Barclays' share price, its firepower to grow the business and, as yesterday's dramatic announcement shows, the life expectancy of its chief executive. His departure may presage yet more turbulent times for the bank, perhaps even surrender to a larger rival with deeper pockets. Yesterday, as one worker scurried into Barclays headquarters, that was not the issue uppermost in the mind.
"I haven't really thought about Martin Taylor, I'm more interested in what I'm having for lunch," he said. The City is that kind of place.