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Two dimensional distributions of T90 versus Epeak (or Ebreak) for three bright GRB samples have been investigated. The result shows that although both T90 and Epeak (or Ebreak) each span over a wide range, they are restricted to the region log(T90) ＜ -log(Epeak) + 5.24. This cannot be explained by the current fireball model. It may represent a constraint on the fireball model.