Toyota dropped their appeal against Ralf Schumacher being stripped of a point in Sunday's San Marino Grand Prix.
The decision, announced by the Formula One team on Friday, confirmed Germany's Nick Heidfeld as the eighth placed and final points-scoring driver for Williams and relegated compatriot Schumacher to 11th.
"The team lodged an appeal on the evening of the race because it wanted the opportunity to undertake a detailed analysis of the incident," Toyota said in a statement.
"After an exhaustive review of the data, the team feels that the evidence is not conclusive and has decided not to take the matter further."
The hearing had been scheduled for Paris on Tuesday, the day before one involving BAR that could see heavy sanctions for that team and further amendment to the results with Briton Jenson Button in danger of losing third place.
Toyota added: "The team will however work together with the FIA and other teams to further clarify what constitutes the 'safe release' of the car by the competitor following a pitstop at the subsequent team managers' meeting."
Schumacher was handed a 25-second penalty for what stewards deemed was his unsafe exit from a pitstop during the race at Imola.
Toyota remain second in the championship.
The BAR hearing pits the governing International Automobile Federation (FIA) against its own stewards, who confirmed Button's podium on Sunday night after six hours of deliberations.
There has been speculation that BAR might have used a second, concealed fuel tank to enable Button to run light during the race.
BAR have said they have nothing to hide and have denied running below the minimum weight at any stage of the race.
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