An effective backbone network is important to deep learning-based Deformable Medical Image Registration (DMIR), because it extracts and matches the features between two images to discover the mutual correspondence for fine registration. However, the existing deep networks focus on single image situation and are limited in registration task which is performed on paired images. Therefore, we advance a novel backbone network, XMorpher, for the effective corresponding feature representation in DMIR. 1) It proposes a novel full transformer architecture including dual parallel feature extraction networks which exchange information through cross attention, thus discovering multi-level semantic correspondence while extracting respective features gradually for final effective registration. 2) It advances the Cross Attention Transformer (CAT) blocks to establish the attention mechanism between images which is able to find the correspondence automatically and prompts the features to fuse efficiently in the network. 3) It constrains the attention computation between base windows and searching windows with different sizes, and thus focuses on the local transformation of deformable registration and enhances the computing efficiency at the same time. Without any bells and whistles, our XMorpher gives Voxelmorph 2.8% improvement on DSC, demonstrating its effective representation of the features from the paired images in DMIR. We believe that our XMorpher has great application potential in more paired medical images. Our XMorpher is open on https://github.com/Solemoon/XMorpher