Teaching my children to get along with one another

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I have three children ages 8, 4, and 4. They get along at times, but they seem to fight several times a day over silly stuff or one will just pick on the others just to make them mad. I have tried time outs and separating them. I have tried to reward them for good behavior, but nothing seems to work for very long. I had this fantasy that my children would be loving and caring to one another naturally, but that is not happening in my house. Do your kids get along? Any suggestions?