Complex genetic disorders are a result of a combination of genetic and nongenetic factors, all potentially interacting. Machine learning methods hold the potential to identify multilocus and environmental associations thought to drive complex genetic traits. Decision trees, a popular machine learning technique, offer a computationally low complexity algorithm capable of detecting associated sets of single nucleotide polymorphisms (SNPs) of arbitrary size, including modern genome‐wide SNP scans. However, interpretation of the importance of an individual SNP within these trees can present challenges. We present a new decision tree algorithm denoted as Bagged Alternating Decision Trees (BADTrees) that is based on identifying common structural elements in a bootstrapped set of Alternating Decision Trees (ADTrees). The algorithm is order , where n is the number of SNPs considered and k is the number of SNPs in the tree constructed. Our simulation study suggests that BADTrees have higher power and lower type I error rates than ADTrees alone and comparable power with lower type I error rates compared to logistic regression. We illustrate the application of these data using simulated data as well as from the Lupus Large Association Study 1 (7,822 SNPs in 3,548 individuals). Our results suggest that BADTrees hold promise as a low computational order algorithm for detecting complex combinations of SNP and environmental factors associated with disease.