Genome-wide association studies (GWASs) aim to identify genetic susceptibility to complex diseases by assaying and analyzing hundreds of thousands of single nucleotide polymorphisms (SNPs). Although traditional single-locus statistical tests have identified many genetic determinants of susceptibility, those findings cannot completely explain genetic contributions to complex diseases. Marchini and coauthors demonstrated the importance of testing two-locus associations allowing for interactions through a wide range of simulation studies. However, such a test is computationally demanding as we need to test hundreds of billions of SNP pairs in GWAS. Here, we provide a method to address this computational burden for dichotomous phenotypes.