Image attribute editing focuses on editing specific attribute according to text prompts while preserving other attributes in the source image. Previous methods often struggle to find the accurate editing direction, leading to insufficient editing or undesired modifications. In this paper, we search for the editing direction in a subspace, greatly improving the efficiency and accuracy. We use the pullback method to find local latent bases in the tangent space and learn the combination coefficients of these bases, achieving the desired editing result with just one step of training. Moreover, we apply a novel contrastive loss to alleviate the issues of insufficient editing and undesired modifications. Our method does not require domain-specific pre-trained models or additional training data, yet with the ability of open-domain editing. Experiments on various datasets demonstrate that our method can accurately modify the target attribute while preserving the other attributes of the source image, indicating that our method can find a more accurate direction for image attribute editing.