Brain aging is a complex and heterogeneous process characterized by the selective loss and preservation of brain functions. This study examines the normal aging effects on the cerebral cortex by characterizing changes in functional connectivity using resting-state fMRI data. Previous resting-state fMRI studies on normal aging have examined specific networks of the brain, whereas few studies have examined cortical-cortical connectivities across the entire brain. To characterize the effects of normal aging on the cerebral cortex, we proposed the Pearson functional product-moment correlation coefficient for measuring functional connectivity, which has advantages over the traditional correlation coefficient. The distinct patterns of changes in functional connectivity within and among the four cerebral lobes clarified the effects of normal aging on cortical function. Besides, the advantages of the proposed approach over other methods considered were demonstrated through simulation comparisons. The results showed heterogeneous changes in functional connectivity in normal aging. Specifically, the elderly group exhibited enhanced inter-lobe connectivity between the frontal lobe and the other lobes. Inter-lobe connectivity decreased between the temporal and parietal lobes. The results support the frontal aging hypothesis proposed in behavioral and structural MRI studies. In conclusion, functional correlation analysis enables differentiation of changes in functional connectivities and characterizes the heterogeneous aging effects in different cortical regions.