With the increasing amount of HD or even UHD video, the video streaming transmission over the mobile network is confronted with various quality of experience issues. To facilitate the delivery of compressed video over the network, it is extremely helpful to further compress the coded video bit stream without any information loss, so-called lossless recompression. However, the existing lossless video/image compression algorithms aim to remove the pixel-domain (e.g., lossless coding mode of HEVC) or the coefficient-domain (e.g., entropy coding) redundancy rather than the bit-stream-domain redundancy. To this end, we propose a novel lossless recompression approach to eliminate statistical redundancy in the coded video bit stream. The core idea is to increase the probability of this repetitive pattern of continuous “0” or “1” symbol strings in the binary symbol sequence by rearranging the sequence, including value mapping and position aggregation. In particular, Fibonacci-based mapping rule is used to convert the original sequence (those binary symbols in Fibonacci positions) into a new one with more continuous “0” or “1.” Besides, we aggregate as many identical symbols as possible together to further increase the probability of the occurrence of repetitive patterns. Finally, the lossless compression algorithm and the asymptotic lossless compression scheme are designed to achieve a compact representation of the rearranged symbol sequence. We also regulate formal syntactic structures for the proposed mapping rule, aggregation algorithm, and recompression scheme so as to deterministically revert from the recoded version to the original bit stream. The experimental results on compressed H.264/AVC and H.265/HEVC video data show that our approach can considerably reduce the bit rate of streaming video.