Motivation: Epistasis, the context-dependence of the contribution of an amino acid substitution to fitness, is common in evolution. To detect epistasis, fitness must be measured for at least four genotypes: the reference genotype, two different single mutants and a double mutant with both of the single mutations. For higher-order epistasis of the order n, fitness has to be measured for all 2n genotypes of an n-dimensional hypercube in genotype space forming a ‘combinatorially complete dataset’. So far, only a handful of such datasets have been produced by manual curation. Concurrently, random mutagenesis experiments have produced measurements of fitness and other phenotypes in a high-throughput manner, potentially containing a number of combinatorially complete datasets. Results: We present an effective recursive algorithm for finding all hypercube structures in random mutagenesis experimental data. To test the algorithm, we applied it to the data from a recent HIS3 protein dataset and found all 199 847 053 unique combinatorially complete genotype combinations of dimensionality ranging from 2 to 12. The algorithm may be useful for researchers looking for higher-order epistasis in their high-throughput experimental data.