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We propose a novel one-step transformer-based person search framework, PSTR, that jointly performs person detection and re-identification (re-id) in a single architecture. PSTR comprises a person search-specialized (PSS) module that contains a detection encoder-decoder for person detection along with a discriminative re-id decoder for person re-id. The discriminative re-id decoder utilizes a multi-level supervision scheme with a shared decoder for discriminative re-id feature learning and also comprises a part attention block to encode relationship between different parts of a person. We further introduce a simple multi-scale scheme to support re-id across person instances at different scales. PSTR jointly achieves the diverse objectives of object-level recognition (detection) and instance-level matching (re-id). To the best of our knowledge, we are the first to propose an end-to-end one-step transformer-based person search framework. Experiments are performed on two popular benchmarks: CUHK-SYSU and PRW. Our extensive ablations reveal the merits of the proposed contributions. Further, the proposed PSTR sets a new state-of-the-art on both benchmarks. On the challenging PRW benchmark, PSTR achieves a mean average precision (mAP) score of 56.5%. The source code is available at \url{https://github.com/JialeCao001/PSTR}.