Text-to-video editing aims to edit the visual appearance of a source video conditional on textual prompts.A major challenge in this task is to ensure that all frames in the edited video are visually consistent. Most recent works apply advanced text-to-image diffusion models to this task by inflating 2D spatial attention in the U-Net into spatio-temporal attention.Although temporal context can be added through spatio-temporal attention, it may introduce some irrelevant information for each patch and therefore cause inconsistency in the edited video. In this paper, for the first time, we introduce optical flow into the attention module in diffusion model's U-Net to address the inconsistency issue for text-to-video editing.Our method, FLATTEN, enforces the patches on the same flow path across different frames to attend to each other in the attention module, thus improving the visual consistency in the edited videos. Additionally, our method is training-free and can be seamlessly integrated into any diffusion based text-to-video editing methods and improve their visual consistency.Experiment results on existing text-to-video editing benchmarks show that our proposed method achieves the new state-of-the-art performance. In particular, our method excels in maintaining the visual consistency in the edited videos.