While the influence of cross-sectional β-amyloid (Aβ) on longitudinal changes in cognition is well established, longitudinal change-on-change between Aβ and cognition is less explored. A series of bivariate latent change score models (LCSM) examined the relationship between changes in 11C-Pittsburgh Compound-B (PiB) positron emission tomography (PET) and the Preclinical Alzheimer's Cognitive Composite-5 (PACC-5) while adjusting for covariates, including cross-sectional medial temporal lobe (MTL) tau-PET burden. We selected 352 clinically normal older participants with up to 9 years of PiB-PET and PACC-5 data from the Harvard Aging Brain Study (HABS). Aβ accumulation was associated with subsequent cognitive decline beyond the effects of cross-sectional Aβ burden. Within this model including covariates such as age, sex, and apolipoprotein ε4 (APOEε4) status, we found no evidence supporting previously published associations between cross-sectional tau-PET and cognitive intercept/slope. Short-term Aβ changes are significantly associated with cognitive decline in clinically normal older adults and may eclipse the effect of cross-sectional Aβ and MTL tau. Aβ accumulation is associated with subsequent cognitive decline. High Aβ burden is not the sole metric signaling impending cognitive decline. Contrary to prior work, MTL tau-PET and cognition were not associated in our models. Models of bivariate latent Aβ and cognitive change may eclipse theeffects of MTL tau.