Over the past few years, several approaches have been proposed to assist in the early diagnosis of Alzheimer's disease (AD) and its prodromal stage of mild cognitive impairment (MCI). For solving this high dimensional classification problem, the widely used algorithm remains to be Support Vector Machines (SVM). But due to the high variance of the data, the classification performance of SVM remains unsatisfactory, especially for delineating the MCI group from the cognitively normal control (CN) group. This study introduces a novel algorithm based on the Gaussian discriminant analysis (GDA) for a more effective and accurate classification performance. Subjects considered in this study included 190 CN, 305 MCI, and 133 AD subjects. Using 75% of the data as the training set with a tenfold cross validation, the proposed algorithm achieved an average accuracy of 94.17%, a sensitivity of 93.00%, and a specificity of 95.00% for discriminating AD from CN; and an average accuracy of 84.86%, a sensitivity of 84.78%, and a specificity of 85.00% for discriminating MCI from CN. Then a true test was implemented for the remaining 25% data, for discriminating specifically MCI from CN, resulting in an accuracy of 82.20%, a sensitivity of 83.10%, and a specificity of 80.85%. As revealed through the literature, these results involving the delineation of the MCI group from CN could be considered as the best classification performance obtained so far. This study also shows that by separating left and right hemispheres of the brain into two decision spaces, then combining the results of these two spaces, the classification performance can be improved significantly; an assertion proven in this study.