A method is presented for conducting a Hayman analysis of non-replicated diallel tables using a maximum-likelihood (ML) model-fitting approach, rather than a traditional analysis of variance (ANOVA) approach. Hayman's linear model for a diallel analysis is used to generate a table of expected cell means. This table of expected cell means is fit to a table of observed cell means, and the fit is assessed using a chi-square value. Often data collected from diallel crosses fail to meet the underlying assumptions of ANOVA. The ML method makes no assumptions about equal cell sizes or homogeneity of variance. Thus, the ML method for diallel analysis provides some statistical advantages over ANOVA methods. The ML method also offers the advantage of having the ability to analyze diallels with missing cells. Using the ML method, incomplete diallel tables can be analyzed, and the partitioning of all the sources of variation in a diallel table is still accomplished from the remaining crosses. These advantages make the ML method an attractive approach for extracting the maximum amount of information from a diallel table.