This paper reveals a characteristic of DEtection Transformer (DETR) that negatively impacts its training efficacy, i.e., the cross-attention and self-attention layers in DETR decoder have contrary impacts on the object queries (though both impacts are important). Specifically, we observe the cross-attention tends to gather multiple queries around the same object, while the self-attention disperses these queries far away. To improve the training efficacy, we propose a Divide-And-Conquer DETR (DAC-DETR) that divides the cross-attention out from this contrary for better conquering. During training, DAC-DETR employs an auxiliary decoder that focuses on learning the cross-attention layers. The auxiliary decoder, while sharing all the other parameters, has NO self-attention layers and employs one-to-many label assignment to improve the gathering effect. Experiments show that DAC-DETR brings remarkable improvement over popular DETRs. For example, under the 12 epochs training scheme on MS-COCO, DAC-DETR improves Deformable DETR (ResNet-50) by +3.4 AP and achieves 50.9 (ResNet-50) / 58.1 AP (Swin-Large) based on some popular methods (i.e., DINO and an IoU-related loss). Our code will be made available at https://github.com/huzhengdongcs/DAC-DETR.