The authors present a secure facial recognition system. The biometric data are transformed to the cancellable domain using high-order polynomial functions and co-occurrence matrices. The proposed method has provided both high-recognition accuracy and biometric data protection. Protection of data relies on the polynomial functions, where the new reissued cancellable biometric can be obtained by changing the polynomial parameters. Besides the protection of data, the reconstructed co-occurrence matrices also contributed to the accuracy enhancement. Hadamard product is used to reconstruct the new measure and has shown high flexibility in proving a new relationship between two independent covariance matrices. The proposed cancellable biometric is treated in the same manner as the original biometric data, which enables replacement of original data by the novel cancellable algorithm with no change to the authentication system. The two-dimensional principal component analysis recognition algorithm is used at the authentication stage. Results have shown high non-reversibility of data with improved accuracy over the original data and raised the performance recognition rate to 97.