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Within the frameworks of the well-known contract net protocol, a task allocation method for multi-robot cooperative hunting behavior is proposed based on an improved auction algorithm. Previous allocation methods using ordinary auction algorithms might turn out to be unsuitable when targets keep moving. Furthermore, the ordinary auctions might lead to unfavorable releases of the captured targets, because the hunters which were formerly assigned to relative tasks might be designated to some other tasks in a new round of bidding. In this paper an improved auction algorithm is proposed which may establish an ordered task list and holds biddings for each task in the list repeatedly. Therefore the allocation methods can be modified which allow dealing with a considerable volume of tasks in a dynamic environments. In addition, this approach holds no biddings for the accomplished tasks, and the relative hunters will keep guarding on their previously assigned target. The improvements also save the computational cost. Simulations demonstrate the flexibility and the efficiency of the method and the hunting task can be achieved in nearly half the time of the original methods.