Abstract: Models based on generative adversarial network(GAN)can generate very realistic face images,which bring additional challenges to justice,criminal investigation and reputation protection,etc.Therefore,a GAN-generated face detection algorithm having a strong generalization ability is proposed by using quaternions.The algorithm consists of a GAN noise fingerprint extraction module and a classification module.The former module uses Siamese quaternion U-Net to extract fingerprint features.The latter module adopts quaternion ResNet to distinguish the natural face from the GAN-generated face based on the extracted fingerprint features.In addition,the distance based logistic loss and cross entropy loss are used to optimize parameters.Experiments are based on a public natural face dataset CelebA,and some generated face datasets that generated by various GANs trained on the CelebA.Four groups of ablation experiments verify the improvements of the proposed algorithm in four aspects.The experiments,in which training data generated by only one kind of GAN but testing data by multiple GANs,show that the proposed algorithm has stronger generalization ability than the existing algorithms.Robustness experiments show that the proposed algorithm is also robust against JPEG attacks.