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In this paper, we propose a novel face image hashing method based on an optimal linear transformation. In the proposed method, first, we apply a feature extraction method. Then, we define an optimal linear transformation matrix based on within-class covariance matrix which is the maximum likelihood estimate of the variations of the biometric data belonging to the same user. Next, we reduce the dimension of the feature vector by using this transform. Finally, we apply quantization and obtain a face image hash vector. We test the performance of the proposed method with AT&T and M2VTS face databases and compare the results with the random projection based biometric hashing methods. We perform the simulations by taking into account two scenarios: 1) Secret key is not known by attacker, 2) Attacker illegally acquires the secret key. The simulation results show the proposed method has better performance especially when the secret key has been compromised.