This paper demonstrates the use of non-linear decomposition for identifying discrimination in referral to a cardiac rehabilitation (CR) program. The application is important because the methods are not commonly applied in this context. A secondary data analysis was conducted on a cohort of 2375 patients eligible for referral (as defined) to an Australian hospital outpatient CR program (1 July 1996 to 31 December 2000) on the basis of inpatient discharge diagnosis codes. Data from a population-based disease register were linked to hospital inpatient statistics and CR program records. Cohort selection was established in accordance with first register recorded hospital separations having specified cardiac inpatient diagnoses for which CR was recommended. Using the existing literature as a guide, multivariate logistic regression methods tested the strength of statistical association between independent variables (or 'endowments') and CR referral. Compared with males, females had 40% fewer odds of being referred. Non-linear decomposition was performed as a post-logistic regression technique to show the extent to which the sex-based inequality in referral (as defined here) was due to group characteristics (the relative distribution of endowments) compared with other influences not adjusted for in the model. The results showed that approximately 18% of the male-female inequality in referral was not explained by group characteristics, and on this basis was 'discriminatory'. The extent to which individual endowments contributed to the explained part of the inequality was also of interest. The methods offer potentially useful tools for informing researchers, policy makers, clinicians and others about unfair discriminatory processes that influence access to health and social services.