Britain's broadcasting watchdog criticised the BBC on Monday after Jeremy Clarkson, presenter of motoring programme Top Gear, used an "offensive racial term" in an episode on Myanmar.
Regulator Ofcom said that Clarkson's use of the word "slope", as slang for a person of Asian origin, was potentially offensive and that the BBC had failed in its duty to viewers by broadcasting it.
The ruling comes just three months after Clarkson was forced to apologise over footage in which he appeared to use another racist term as part of an old nursery rhyme during filming of Top Gear.
The show has previously got into hot water over its depictions of Mexicans, Albanians, Romanians and Germans.
The latest incident involved a two-part special on Myanmar, also known as Burma, featuring Clarkson and co-presenters Richard Hammond and James May crossing the country in trucks to build a makeshift bridge over the River Kwai.
As the team admired the finished bridge an Asian man is seen to cross it and Clarkson remarks: "That is a proud moment...but... there is a slope on it."
Hammond, taking up the literal meaning of "slope", replied: "You are right, it is definitely higher on that side."
Ofcom said it deemed that Clarkson "deliberately employed the offensive word to refer to the Asian person crossing the bridge as well as the camber of the bridge."
"After a thorough investigation, Ofcom has found the BBC breached broadcasting rules by including an offensive racial term in Top Gear, which was not justified by context," the regulator said.
"Jeremy Clarkson used the word 'slope' to refer both to an Asian man crossing a bridge, and the incline of the bridge. This was scripted in advance. The BBC failed to take the opportunity, either during filming or post-production, to check whether the word had the potential to offend viewers."
The BBC, the world's largest public broadcaster, said on Monday it "unreservedly" repeated an earlier statement after the show aired in March "apologising for the use of the word and for any offence which its use caused".
At the time it had had argued that programme-makers believed the term was "mere slang" and were "were not aware at the time that it had the potential to cause offence".
The BBC issued Clarkson with what he said was a final warning over the previous Top Gear incident when he denied using the N-word while reciting a traditional nursery rhyme.