This paper views the DETR's non-duplicate detection ability as a competition result among object queries. Around each object, there are usually multiple queries, within which only a single one can win the chance to become the final detection. Such a competition is hard: while some competing queries initially have very close prediction scores, their leading query has to dramatically enlarge its score superiority after several decoder layers. To help the leading query stands out, this paper proposes EASE-DETR, which eases the competition by introducing bias that favours the leading one. EASE-DETR is very simple: in every intermediate decoder layer, we identify the ''leading / trailing'' relationship between any two queries, and encode this binary relationship into the following decoder layer to amplify the superiority of the leading one. More concretely, the leading query is to be protected from mutual query suppression in the self-attention layer and encouraged to absorb more object features in the cross-attention layer, therefore accelerating to win. Experimental results show that EASE-DETR brings consistent and remarkable improvement to various DETRs.