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The resting-state functional magnetic resonance imaging (rs-fMRI) modality has gained widespread acceptance as a promising method for analyzing a variety of neurological and psychiatric diseases. It is established that resting-state neuroimaging data exhibit fractal behavior, manifested in the form of slow-decaying auto-correlation and power-law scaling of the power spectrum across low-frequency components. With this property, the rs-fMRI signal can be broken down into fractal and nonfractal components. The fractal nature originates from several sources, such as cardiac fluctuations, respiration and system noise, and carries no information on the brain’s neuronal activities. As a result, the conventional correlation of rs-fMRI signals may not accurately reflect the functional dynamic of spontaneous neuronal activities. This problem can be solved by using a better representation of neuronal activities provided by the connectivity of nonfractal components. In this work, the nonfractal connectivity of rs-fMRI is used to distinguish Alzheimer’s patients from healthy controls. The automated anatomical labeling (AAL) atlas is used to extract the blood-oxygenation-level-dependent time series signals from 116 brain regions, yielding a 116 × 116 nonfractal connectivity matrix. From this matrix, significant connections evaluated using the p-value are selected as an input to a classifier for the classification of Alzheimer’s vs. normal controls. The nonfractal-based approach provides a good representation of the brain’s neuronal activity. It outperformed the fractal and Pearson-based connectivity approaches by 16.4% and 17.2%, respectively. The classification algorithm developed based on the nonfractal connectivity feature and support vector machine classifier has shown an excellent performance, with an accuracy of 90.3% and 83.3% for the XHSLF dataset and ADNI dataset, respectively. For further validation of our proposed work, we combined the two datasets (XHSLF+ADNI) and still received an accuracy of 90.2%. The proposed work outperformed the recently published work by a margin of 8.18% and 11.2%, respectively. Full article