Abstract: Supernet is a core component in many recent Neural Architecture Search (NAS) methods. It not only helps embody the search space but also provides a (relative) estimation of the final performance of candidate architectures. Thus, it is critical that the top architectures ranked by a supernet should be consistent with those ranked by true performance, which is known as the order-preserving ability.In this work, we analyze the order-preserving ability on the whole search space (global) and a sub-space of top architectures (local), and empirically show that the local order-preserving for current two-stage NAS methods still need to be improved.To rectify this, we propose a novel concept of $\textbf{Supernet Shifting}$, a refined search strategy combining architecture searching with supernet fine-tuning. Specifically, apart from evaluating, the training loss is also accumulated in searching and the supernet is updated every iteration. Since superior architectures are sampled more frequently in evolutionary searching, the supernet is encouraged to focus on top architectures, thus improving local order-preserving.Besides, a pre-trained supernet is often un-reusable for one-shot methods. We show that Supernet Shifting can fulfill transferring supernet to a new dataset. Specifically, the last classifier layer will be unset and trained through evolutionary searching. Comprehensive experiments show that our method has better order-preserving ability and can find a dominating architecture. Moreover, the pre-trained supernet can be easily transferred into a new dataset with no loss of performance. Source code will be made public available.