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Biometric authentication and privacy protection are conflicting issues in a practical system. Since biometrics cannot be revoked or canceled if compromised duo to the permanent association with the user, privacy-preserving biometric recognition is desired. However, the recently proposed template protection schemes are not yet sufficiently mature. Specially, the popular noninvertible transform approach will result in an obvious decrease of GAR for a fixed FAR. In this paper, we put forward a novel anonymous fingerprint recognition scheme, Biomapping, as the first approach to integrate the feature extraction, noninvertible transform, and anonymous query as a whole. Biomapping extracts the fingerprint feature utilizing a minutiae-centered region encoding, then performs anonymous enrollment and verification using the noninvertible and discriminable constructions. Experiments on the public domain database show Biomapping can provide better recognition accuracy along with the ability to protect the biometric template, thus becomes a promising solution for privacy trustworthy biometric applications.