Jenson Button and Takuma Sato will return at the European GP
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BAR have sought to end the row over their two-race ban by accepting they did misinterpret Formula One rules.
The FIA, motorsport's world governing body, punished BAR for running an underweight car at the San Marino GP.
BAR criticised the severity of the ban but have now taken a conciliatory stance after being threatened with further punishment by the FIA.
"BAR Honda accept the decision of the FIA Court of Appeal as fair in the circumstances," said a statement.
Button finished third at Imola but his car was found to have a secondary fuel tank, which when drained left the BAR 5.4kg under the minimum 600kg weight limit.
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BAR Honda recognise that the judges in this, as in other cases, are fully independent
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The San Marino stewards originally decided not to take any action against Button but the FIA appealed against the decision.
The FIA appeal court also stripped BAR of the 10 points won by Button and team-mate Takuma Sato at the race.
BAR reacted angrily to the ban but the FIA threatened to punish the team further if they were found to have brought the sport into disrepute by arguing against their suspension.
But BAR's statement added: "Having investigated the matter fully, including making extensive enquiries of other teams, BAR Honda now accept that Formula One cars must always weigh more than 600kg when completely empty of fuel.
"This applies even if the car's fuel system is such that some of the fuel in the car is unusable.
"Before making these enquiries it was the team's honest belief that fuel which could not be used during the race did not have to be removed before the car was weighed.
"BAR Honda recognise that the judges in this, as in other cases, are fully independent, being lawyers and professional judges of high standing who give their service on a voluntary basis.
"BAR Honda want nothing more than to compete with other teams in the Formula One World Championship on an entirely fair and equal basis and look forward to rejoining the competition at the European Grand Prix."