Motivation: Genome-wide association studies show that variants in individual genomic loci alone are not sufficient to explain the heritability of complex, quantitative phenotypes. Many computational methods have been developed to address this issue by considering subsets of loci that can collectively predict the phenotype. This problem can be considered a challenging instance of feature selection in which the number of dimensions (loci that are screened) is much larger than the number of samples. While currently available methods can achieve decent phenotype prediction performance, they either do not scale to large datasets or have parameters that require extensive tuning. Results: We propose a fast and simple algorithm, Macarons, to select a small, complementary subset of variants by avoiding redundant pairs that are likely to be in linkage disequilibrium. Our method features two interpretable parameters that control the time/performance trade-off without requiring parameter tuning. In our computational experiments, we show that Macarons consistently achieves similar or better prediction performance than state-ofthe-art selection methods while having a simpler premise and being at least two orders of magnitude faster. Overall, Macarons can seamlessly scale to the human genome with 107 variants in a matter of minutes while taking the dependencies between the variants into account. Availabilityand implementation: Macarons is available in Matlab and Python at https://github.com/serhan-yilmaz/macarons.