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The Stoke City forward, 32, limped off after 64 minutes of Monday's 1-1 Group E draw with Sweden in Paris.
Walters has not trained since and his absence for the Belgium game was confirmed on Friday.
West Brom midfielder James McClean, Walters' replacement against Sweden, is expected to start in Bordeaux.
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Belgium - ranked second in the world - lost 2-0 to Italy in their opening game.
Italy, who beat Sweden 1-0 on Friday to seal their progress into the last 16, take on the Republic in Lille next Wednesday.
"He thinks he is going to be able to make the Italian game," O'Neill said of Walters on Wednesday.
Wes Hoolahan's opener for the Republic against Sweden at the Stade de France was cancelled out by a Ciaran Clark own goal.
"If that performance doesn't lift you, nothing will," said O'Neill.
"We will have to show the same attitude again, go and compete and be strong on the ball."
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Well it's worked as a game at least, the Angry Birds app was the first to get 500 million downloads.
So inevitably its makers Rovio are now dipping their toes into the world of film.
An animated feature is set for release in 2016, and they've just announced the cast.
The main character "Red" is set to be played by Jason Sudeikis, and in his first role since Frozen, Josh Gad will play Speedy Chuck.
Arguably the most useful bird, the Bomb, will be played by Danny McBride, who appeared in This is the End with Seth Rogan last year. Bill Hader however, will be on the receiving end of the birds' anger after joining the Pork Side.
Maya Rudolph will act the role of Matilda, and the smooth-talking Tyrion Lannister, or Peter Dinklage, will swap the Game of Thrones set for providing the voice of the Mighty Eagle.
There are a number of supporting roles being added to the flock too, including the YouTube stars Smosh (Ian Andrew Hecox and Anthony Padilla), who have more than 30 million subscribers.
While it might be Rovio's first go at films, they've already enjoyed screen success with their recent animated TV series notching up more than 3 billion views in its first 18 months.
The film's producer Josh Cohen says: "I'm extremely proud of this cast.
"These are some of the funniest people out there today, and we're thrilled to have them all on board."
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A search is continuing for four other people missing at the site.
Reports say an initial collapse caused a crane to fall, bringing down more of the multi-storey building.
At least 20 people were treated for injuries following the incident in Ramat Hahayil, a commercial area in the north of the city.
Pictures from the scene show clouds of dust rising from a huge crater, with large amounts of debris at the bottom.
Dozens of firefighters, rescue and security services were dispatched to the site to help the injured and search for those feared missing.
Israel's Haaretz newspaper quoted a fire service spokesman as saying there were "people buried beneath the sand".
Police moved people away from the area, fearing other parts of the building might also collapse.
Republic of Ireland striker Jonathan Walters has been ruled out of Saturday's Euro 2016 clash against Belgium because of an Achilles injury.
[NEXT_CONCEPT]
It's your classic storyline, a group of different birds hurling themselves towards different structures to take out some green piggies.
[NEXT_CONCEPT]
The death toll after a car park collapsed while under construction in the Israeli city of Tel Aviv has risen to three, rescue workers say.