Mr Wagoner's choice of transport did not go down well in Washington
General Motors has asked the US Federal Aviation Administration (FAA) not to allow tracking of its private jets.
The call comes after the company's boss flew to Washington in a jet to ask for $25bn (£16.3bn;19.7bn euros) of public money to bail-out the US car industry.
Chief executive Rick Wagoner was taken to task at a special Senate hearing and pilloried in the worldwide media for such extravagance and poor judgement.
"Couldn't you have downgraded to first class?" said Democrat Gary Ackerman.
GM has subsequently returned two of its fleet - reportedly five strong - of private jets.
The carmaker made the request to the FAA despite insisting this week that Mr Wagoner will not repeat the mistake when he returns to Washington for further discussions about the bail-out next week.
"We availed ourselves of the same option as others have," said GM spokesman Greg Martin.
Rival carmakers Ford and Chrysler, whose chief executives also flew to Washington in separate jets, have kept a much lower profile since the hearing.
All three companies are desperate for funds to help stave off potential bankruptcy.
Sales have plummeted due to the credit crunch and the economic slowdown, and they are burning through billions of dollars in cash each month.
With little or no ability to raise capital in the private markets, they have been forced to go cap in hand to the government.
GM has warned that it could run out of cash in a matter of weeks and cannot wait until President-elect Barack Obama - who has promised to help the industry - is sworn in in January.