Mr Tapie won a much bigger payout than he might have expected in court.
Tapie is flirting with an outfit that faces incredibly serious legal challenges along with formidable financial ones.
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Ms Lagarde decided to use arbitration to settle a long-running legal battle between the state and Mr Tapie.
Speaking on French Europe 1 radio, Mr Tapie said he was "not at all worried" about the investigation.
Ms Lagarde was involved in a dispute between French businessman Bernard Tapie and the bank Credit Lyonnais in 2007.
So did Bernard Tapie, a crooner turned soccer club owner and Socialist minister.
Soon after the bank sold on that stake for a much bigger profit, Mr Tapie claimed they had defrauded him.
At the time Mr Tapie was in the midst of a court battle with the former state-owned bank Credit Lyonnais.
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The settlement Mr Tapie received is believed to be a far greater sum than he would likely have received from the courts.
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The probe relates to her time as French finance minister and her involvement in the payment of compensation to businessman Bernard Tapie.
Ms Lagarde is to be questioned before a magistrate in May over her role in the awarding of financial compensation to businessman Bernard Tapie in 2008.
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The BBC's Christian Fraser, in Paris, says investigators suspect Mr Tapie was granted a deal in return for his support of President Sarkozy in the 2007 election.
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The case stretches back to 1993 when Mr Tapie, a colourful, controversial character in the French business world, sold his stake in sports company Adidas to Credit Lyonnais.
Some months later, the new Finance Minister, Ms Lagarde, overruled objections from her officials and intervened in the judicial case, pushing the bank and Mr Tapie into binding arbitration.
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She referred the case to an arbitration panel, after which Mr Tapie switched his support to Nicholas Sarkozy, then leader of Ms Lagarde's UMP party, in the presidential election campaign.
Mr Tapie was a supporter of ex-President Nicolas Sarkozy.
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The Tapie affair aside, Lagarde largely avoided controversy.
Mr Tapie, who has long been active in French business, sporting and political circles, sued Credit Lyonnais over its handling of the sale in 1993 of sportswear brand Adidas, in which he was a majority stakeholder.
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The Court of Justice of the Republic, which investigates ministerial misconduct, is looking into claims that Mr Tapie, a controversial business figure, may have received favourable treatment because of his support for the former president Nicolas Sarkozy.
She could be placed under formal investigation for the decision to use arbitration, against advice from senior advisers, to settle a long-running court battle between the state and Mr Tapie, a supporter of the then French President, Nicolas Sarkozy.
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