I don't know about innovation, but some companies I know about which are supposedly big and work well...
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Murex (doesn't look too attractive to me, banking solutions... but it's a big company AFAIK)
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Element^n
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Koein: Technically they may not be the best but they have many "big" clients
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CME: Clifton Myers Entreprises Offshore: They have a relatively large group of programmers in Lebanon (by industry standards) working for offshore projects. Challenging... I don't know; it looks somehow like a programming sweatshop from the outside...