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Video - The United States beat Canada in a jump-off
The United States won gold in the team show jumping with three clear rounds in a dramatic jump-off with Canada, while Britain finished seventh.
Canada, who had finished equal on 20 points with the defending champions after the allocated jumps, had to settle for silver in Hong Kong.
Norway secured bronze with 27 points, their best score at an Olympics.
Britain, finishing on 37 points, were left to rue the ineligibility of team anchor John Whitaker for the final.
Whitaker had been expected to jump in the final, even though he had withdrawn from Sunday's first round because of a problem with his horse Peppermill.
Britain were joint fourth after round one and had high hopes of a medal, but shortly before the start of the competition the International Equestrian Federation (FEI) upheld the objections of seven of the other eight national teams competing for medals.
Whitaker's team-mate Tim Stockdale accused some of Britain's rivals of unsporting behaviour, saying: "It is not in the concept of the Olympics.
Perhaps some people saw it as an opportunity to get John out of the competition
"In respect of what John has done for show jumping it is disappointing. Some people should hang their head in shame.
"Medals are at stake, I suppose, and John is good and so people fear him. Perhaps some people saw it as an opportunity to get John out of the competition."
The FEI's decision put enormous pressure on Britain's three remaining riders, who had to compete without the luxury of a discard score, and after a disappointing opening jump by Nick Skelton a top-three finish appeared remote.
Stockdale, on Corlato, then hit two fences for eight penalty points to leave Ben Maher with little to jump for. The 25-year-old produced a magnificent clear final jump on Rolette to move Britain ahead of eighth-placed Sweden and ninth-placed Australia.
Skelton, Stockdale and Maher will compete in the individual show jumping final on Thursday.
One of the performances of the day came from Canada's Ian Millar, at 61 the oldest competitor in the field, who produced a clear round on In Style to force a jump-off.
But the defending champions were impervious to the pressure-cooker atmosphere at the Shatin stadium, with Mclain Ward on Sapphire, Laura Kraut on Cedric and Will Simpson on Carlsson Vom Dach all producing clear rounds.
Canada's Eric Lamaz jumped a faultless round, but Jill Henselwood, the first rider out for the Canadians, effectively lost the gold after picking up four faults on Special Ed.