Big datasets, accumulated from biomedical and agronomic studies, provide the potential to identify genes that control complex human diseases and agriculturally important traits through genome-wide association studies (GWAS). However, big datasets also lead to extreme computational challenges, especially when sophisticated statistical models are employed to simultaneously reduce false positives and false negatives. The newly developed fixed and random model circulating probability unification (FarmCPU) method uses a bin method under the assumption that quantitative trait nucleotides (QTNs) are evenly distributed throughout the genome. The estimated QTNs are used to separate a mixed linear model into a computationally efficient fixed effect model (FEM) and a computationally expensive random effect model (REM), which are then used iteratively. To completely eliminate the computationally expensive REM, we replaced REM with FEM by using Bayesian information criteria. To eliminate the requirement that QTNs be evenly distributed throughout the genome, we replaced the bin method with linkage disequilibrium information. The new method is called Bayesian-information and Linkage-disequilibrium Iteratively Nested Keyway (BLINK). Both real and simulated data analyses demonstrated that BLINK improves statistical power compared to FarmCPU, in addition to remarkably reducing computing time. Now, a dataset with one million individuals and one-half million markers can be analyzed within three hours, instead of one week using FarmCPU.