The feature matching problem is a fundamental problem in various areas of computer vision including image registration, tracking and motion analysis. Rich local representation is a key part of efficient feature matching methods. However, when the local features are limited to the coordinate of key points, it becomes challenging to extract rich local representations. Traditional approaches use pairwise or higher order handcrafted geometric features to get robust matching; this requires solving NP-hard assignment problems. In this paper, we address this problem by proposing a graph neural network model to transform coordinates of feature points into local features. With our local features, the traditional NP-hard assignment problems are replaced with a simple assignment problem which can be solved efficiently. Promising results on both synthetic and real datasets demonstrate the effectiveness of the proposed method.