Epistasis, or gene-gene interaction, results from joint effects of genes on a trait; thus, the same alleles of one gene may display different genetic effects in different genetic backgrounds. In this study, we generalized the coding technique of a natural and orthogonal interaction (NOIA) model for association studies along with gene-gene interactions for dichotomous traits and human complex diseases. The NOIA model which has non-correlated estimators for genetic effects is important for estimating influence from multiple loci. We conducted simulations and data analyses to evaluate the performance of the NOIA model. Both simulation and real data analyses revealed that the NOIA statistical model had higher power for detecting main genetic effects and usually had higher power for some interaction effects than the usual model. Although associated genes have been identified for predisposing people to melanoma risk: HERC2 at 15q13.1, MC1R at 16q24.3 and CDKN2A at 9p21.3, no gene-gene interaction study has been fully explored for melanoma. By applying the NOIA statistical model to a genome-wide melanoma dataset, we confirmed the previously identified significantly associated genes and found potential regions at chromosomes 5 and 4 that may interact with the HERC2 and MC1R genes, respectively. Our study not only generalized the orthogonal NOIA model but also provided useful insights for understanding the influence of interactions on melanoma risk.