Alstom announced in November that the Texas-based outsourcer had been chosen as preferred bidder in what the supplier described as "among the largest IT agreements in the history of manufacturing and energy industries".
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EDS spokesman said the deal was expected to reduce Alstom's technology costs of about $400m (£252m) a year.
Since then, according to Alstom, "the two parties have been unable to reach mutually acceptable terms for the transaction".
EDS was set to manage Alstom's IT infrastructure and applications in 14 countries - Belgium, Brazil, Canada, France, Germany, Italy, Mexico, Poland, Portugal, Spain, Sweden, Switzerland, the UK and US. The deal would have seen 1,300 Alstom employees transferred to EDS.
The failure to secure the contract is a blow to EDS, which last year saw its share price slump after an unprecedented profits warning. The company has lost bids for major outsourcing deals with JP Morgan Chase, the state of Texas and a 10-year $7bn (£4.4bn) contract with Procter & Gamble in recent months.
Alstom said it "continues to favour outsourcing its IT in order to reduce costs".