Copy-move forgery detection is a challenging task in digital image forensics. Keypoint-based detection methods have proven to be very efficient to detect copied-moved forged areas in images. Although these methods are effective, the keypoint matching phase has a high complexity, which takes a long time to detect forgeries, especially for very large images such as 4K Ultra HD images. In this paper, we propose a new keypoint-based method with a new fast feature matching algorithm, based on the generalized two nearest-neighbor (g2NN) algorithm allowing us to greatly reduce the complexity and thus the computation time. First, we extract keypoints from the input image. After ordering them, we perform a match search restricted to a window around the current keypoint. To detect the keypoints, we propose not to use a threshold, which allows low intensity keypoint matching and a very efficient detection of copy-move forgery, even in very uniform or weakly textured areas. Then, we apply a new matching algorithm, and finally we compute the cluster thanks to the DBSCAN algorithm. Our experimental results show that the method we propose can detect copied-moved areas in forged images very accurately and with a very short computation time which allows for the fast detection of forgeries on 4K images.