Many clinical studies have shown that electroencephalograms (EEG) of Alzheimer patients (AD) often have an abnormal power spectrum. In this paper a frequency band analysis of AD EEG signals is presented, with the aim of improving the diagnosis of AD from EEG signals. Relative power in different EEG frequency bands is used as features to distinguish between AD patients and healthy control subjects. Many different frequency bands between 4 and 30Hz are systematically tested, besides the traditional frequency bands, e.g., theta band (4–8Hz). The discriminative power of the resulting spectral features is assessed through statistical tests (Mann-Whitney U test). Moreover, linear discriminant analysis is conducted with those spectral features. The optimized frequency ranges (4–7Hz, 8–15Hz, 19–24Hz) yield substantially better classification performance than the traditional frequency bands (4–8Hz, 8–12Hz, 12–30Hz); the frequency band 4–7Hz is the optimal frequency range for detecting AD, which is similar to the classical theta band. The frequency bands were also optimized as features through leave-one-out crossvalidation, resulting in error-free classification. The optimized frequency bands may improve existing EEG based diagnostic tools for AD. Additional testing on larger AD datasets is required to verify the effectiveness of the proposed approach.