Cycle consistency is widely used for face editing. However, we observe that the generator tends to find a tricky way to hide information from the original image to satisfy the constraint of cycle consistency, making it impossible to maintain the rich details (e.g., wrinkles and moles) of non-editing areas. In this work, we propose a simple yet effective method named HifaFace to address the above-mentioned problem from two perspectives. First, we relieve the pressure of the generator to synthesize rich details by directly feeding the high-frequency information of the input image into the end of the generator. Second, we adopt an additional discriminator to encourage the generator to synthesize rich details. Specifically, we apply wavelet transformation to transform the image into multi-frequency domains, among which the high-frequency parts can be used to recover the rich details. We also notice that a fine-grained and wider-range control for the attribute is of great importance for face editing. To achieve this goal, we propose a novel attribute regression loss. Powered by the proposed framework, we achieve high-fidelity and arbitrary face editing, outperforming other state-of-the-art approaches.