Resting state correlations between voxels in white matter (WM) are demonstrably anisotropic, which has led to the derivation of functional correlation tensors (FCT) to quantify the structure of blood oxygenation level dependent (BOLD) effects in WM tracts. However, the reproducibility of FCTs across brains has not been established, while changes in WM occur with normal aging, development and in neurological disorders. For example, previous research has demonstrated severe age-related changes in the microstructure of the brain, including axonal demyelination in WM. Here we report our analyses of the FCT characteristics of fMRI images of a large cohort of 461 cognitively normal subjects (190 females, 271 males) sourced from the Open Access Series of Imaging Studies (OASIS), with age distributions of 42 y/o – 95 y/o. FCT indices, including axial functional correlations, radial functional correlations, mean functional correlations and fractional anisotropy, were quantified in WM bundles defined by the JHU ICBM-DTI-81 WM atlas, and their variations with normal aging were examined. The results revealed a dimorphic distribution of changes in FCT metrics, with decreases of the functional correlations in some regions and increases in others. Significant correlations between FCT findings and neuropsychological scores were also observed in several WM tracts, indicating relationships between cognitive performances and resting-state correlations. These findings converge to suggest that local functional connectivity of brain WM changes with normal aging in a region-, and age-specific manner.