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In anchor-free object detection, the center regions of bounding boxes are often highly weighted to enhance detection quality. However, the central area may become less significant in some situations. In this paper, we propose a novel dual attention-based approach for the adaptive weight assignment within bounding boxes. The proposed improved dual attention mechanism allows us to thoroughly untie spatial and channel attention and resolve the confusion issue, thus it becomes easier to obtain the proper attention weights. Specifically, we build an end-to-end network consisting of backbone, feature pyramid, adaptive weight assignment based on dual attention, regression, and classification. In the adaptive weight assignment module based on dual attention, a parallel framework with the depthwise convolution for spatial attention and the 1D convolution for channel attention is applied. The depthwise convolution, instead of standard convolution, helps prevent the interference between spatial and channel attention. The 1D convolution, instead of fully connected layer, is experimentally proved to be both efficient and effective. With the adaptive and proper attention, the correctness of object detection can be further improved. On public MS-COCO dataset, our approach obtains an average precision of 52.7%, achieving a great increment compared with other anchor-free object detectors.