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The influence of the apolipoprotein E ε4 allele (APOE4) on brain microstructure of cognitively normal older adults remains incompletely understood, in part due to heterogeneity within study populations. In this study, we examined white-matter microstructural integrity in cognitively normal older adults as a function of APOE4 carrier status using conventional diffusion-tensor imaging (DTI) and the novel orthogonal-tensor decomposition (DT-DOME), accounting for the effects of age and sex. Age associations with white-matter microstructure did not significantly depend on APOE4 status, but did differ between sexes, emphasizing the importance of accounting for sex differences in APOE research. Moreover, we found the DT-DOME to be more sensitive than conventional DTI metrics to such age-related and sex effects, especially in crossing WM fiber regions, and suggest their use in further investigation of white matter microstructure across the life span in health and disease.