In this paper, we describe a biometric hash algorithm for robust extraction of bits from face images. While a face-recognition system has high acceptability, its accuracy is low. The problem arises because of insufficient capability of representing features and variations in data. Thus, we use dimensionality reduction to improve the capability to represent features, error correction to improve robustness with respect to within-class variations, and random projection and orthogonalization to improve discrimination among classes. Specifically, we describe several dimensionality-reduction techniques with biometric hashing enhancement for various numbers of bits extracted. The theoretical results are evaluated on the FERET face database showing that the enhanced methods significantly outperform the corresponding raw methods when the number of extracted bits reaches 100. The improvements of the postprocessing stage for principal component analysis (PCA), Wavelet Transform with PCA, Fisher linear discriminant, Wavelet Transform, and Wavelet Transform with Fourier-Mellin Transform are 98.02%, 95.83%, 99.46%, 99.16%, and 100%, respectively. The proposed technique is quite general, and can be applied to other biometric templates. We anticipate that this algorithm will find applications in cryptographically secure biometric authentication schemes.