The news came in a statement to the Stock Exchange which was forced by a sharp rise in the Williams share price from 27p to 398p yesterday morning on speculation that a deal was imminent. Later the shares retreated to close at 380p, up 7.25p on the day.
Both sides said that the talks, which covered a range of options from joint ventures to full-scale merger, were terminated last week after Williams' chairman Sir Nigel Rudd and Tyco's chairman Dennis Kozolowski failed to agree on a valuation of the business, or the future direction of the two companies.
However, yesterday's statement does not rule out further talks, and a hostile bid by Tyco for Williams remains a possibility although City sources said Tyco has never made a hostile bid, preferring to grow by cooperation and agreement.
Tyco claims to the largest manufacturer and supplier of both fire-protection and electronic security equipment in the world, and has publicly stated its intention to expand outside North America.
In the past 18 months it has taken over both ADT and Thorn Securities.
It has a market capitalisation of $20bn and annual turnover of around $13bn. The fire protection and security division accounts for well under half the group's annual turnover but is roughly the same size and market value as Williams, which has been steadily disposing of its home improvements business to focus on fire protection and security.
The businesses offer a broadly similar range of products and services, but Tyco operates almost exclusively in North America, while more than half of both turnover and profits of Williams are in the UK, Europe, Australasia and Asia.
Williams shares have fallen from a peak of 486p earlier this year, but they have staged a steady recovery from a low point of 313p over the last few weeks, after publishing interim profits for the six months to the end of June.
These showed profits more than doubled to pounds 264m since the half-way stage in the previous year. About a quarter of the increase might have come from Chubb, which has now been fully integrated.