We tackle the efficiency problem of learning local feature matching.Recent advancements have given rise to purely CNN-based and transformer-based approaches, each augmented with deep learning techniques. While CNN-based methods often excel in matching speed, transformer-based methods tend to provide more accurate matches. We propose an efficient transformer-based network architecture for local feature matching.This technique is built on constructing multiple homography hypotheses to approximate the continuous correspondence in the real world and uni-directional cross-attention to accelerate the refinement. On the YFCC100M dataset, our matching accuracy is competitive with LoFTR, a state-of-the-art transformer-based architecture, while the inference speed is boosted to 4 times, even outperforming the CNN-based methods.Comprehensive evaluations on other open datasets such as Megadepth, ScanNet, and HPatches demonstrate our method's efficacy, highlighting its potential to significantly enhance a wide array of downstream applications.