In this paper, we propose a new cross-domain face forgery detection method that is insensitive to different and possibly unseen forgery methods while ensuring an acceptable low false positive rate. Although existing face forgery detection methods are applicable to multiple domains to some degree, they often come with a high false positive rate, which can greatly disrupt the usability of the system. To address this issue, we propose an Contrastive Desensitization Network (CDN) based on a robust desensitization algorithm, which captures the essential domain characteristics through learning them from domain transformation over pairs of genuine face images. One advantage of CDN lies in that the learnt face representation is theoretical justified with regard to the its robustness against the domain changes. Extensive experiments over large-scale benchmark datasets demonstrate that our method achieves a much lower false alarm rate with improved detection accuracy compared to several state-of-the-art methods.