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To achieve high efficiency with limitation of energy consumption is a key problem in the system of UAVs. In existing UAV task allocation methods, the relevance between tasks and UAV cruise directions is neglected, which may further influence the energy consumption and delay of task accomplishment. In view of this, this paper proposed an UAV task allocation method based on the relevance analysis between tasks and cruise directions. This method includes two phases: task screening phase and conflict resolution phase based on consensus. In the first phase, this method selects out tasks without turning back for an UAV according to angles between the cruise direction of the UAV and directions of these tasks, then designs an algorithm to further select candidate tasks before interaction from the tasks without turning back according to their energy consumption utility parameters and time urgency parameters. In the second phase, this method solves tasks conflicts between UAVs after exchanging of their candidate tasks according to energy consumption utility parameters and time delay parameters of these tasks in different cruise directions of these UAVs. Simulation results verify that the proposed method can achieve lower average task energy consumption and average task delay. [ABSTRACT FROM AUTHOR]