"Air France-KLM launched the sale of a block of shares representing 7.5 percent of (Amadeus) capital," an spokesman from the Franco-Dutch carrier said.
Air France-KLM had valued its total 15.22 stake in Amadeus, which provides the technology for airline electronic reservations and ticketing, at about 1.0 billion euros ($1.33 billion).
The operation, valued at around 400 million euros, will align Air France-KLM's participation in Amadeus with other shareholders in the technology group, the spokesman said.
Shares in Amadeus rose 3.0 percent in a slightly rising Madrid stock exchange.
Spanish market authorities had delayed trading in the company' stock when the market opened to avert disruption caused by the divestment announcement.