For 10 years you're in charge of managing the European Union. Then you advise Goldman Sachs on Brexit.

Conflict of interest? More than 130,000 people think so, and they've signed a petition started by EU staff in protest against the bank's recruitment of the former president of the European Commission, Jose Manuel Barroso.

He was hired in July -- after the Brexit vote -- and will advise Goldman Sachs (GS), among other things, on how to limit the damage from the U.K.'s withdrawal from the EU.

The appointment has also drawn a warning from the official charged with investigating complaints into the behavior of EU institutions. Emily O'Reilly wrote to Barroso's successor on Tuesday, saying the move had caused "widespread concerns."

"This public unease will be exacerbated by the fact that Mr Barroso has publicly stated that he will be advising on the U.K.'s decision to leave the EU," O'Reilly said.

Barroso was the top EU official between 2004 and 2014, and Portugal's prime minister before that.

"This decision is a further example of the irresponsible revolving-door practices, which are highly damaging to the EU institutions and, even if not illegal, morally reprehensible," the petition says.

One of the employees who started the petition said he was concerned Barroso's appointment as non-executive chairman of Goldman Sachs International could damage EU interests.

"Euroskeptic politicians have already used Barroso's decision as an argument against the EU," the employee said, speaking on condition of anonymity because of the EU administration's confidentiality rules.

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The petition's authors want Barroso's EU pension to be suspended while he's on Goldman's payroll. They are also asking the EU authorities to take a tougher approach to the work former officials do when they leave office.

Under current EU rules, Barroso was barred from working in the private sector for 18 months after stepping down. That period expired at the end of April. Barroso's appointment with Goldman was announced on July 8, two weeks after the U.K. voted to leave the EU -- the biggest single challenge to European integration for decades.

The critics are not against former officials at the Commission in Brussels getting jobs, but they say they must be seen to behave ethically.

"Coming to Brussels should not be the end of a career, we want the best politicians to come to Brussels...but to work for this particular company at this moment raises many questions," the EU employee said.

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Goldman Sachs said Barroso will "help advise our clients in Europe and around the world on a range of issues."

It said the decision to hire Barroso "had nothing to do with the outcome of the Brexit vote."

"Indeed, we began our discussions at a time when the prevailing view was that the Remain campaign would succeed, an outcome we would have preferred and publicly supported," the bank said in a statement.

Goldman Sachs donated hundreds of thousands of pounds to the campaign to keep Britain in the EU.