To test the null hypothesis of random segregation of marker haplotypes from an unaffected parent to affected offspring for a one-locus autosomal recessive disease, Majumder proposed a test statistic which was shown to be locally most powerful against the alternative hypothesis of non-random segregation due to linkage between the disease and marker loci. The test procedure relied on a chi-squared approximation to the null distribution of the test statistic. In the present study, we show that the chi-squared approximation is poor for most practical situations and derive the exact null distribution of a function of the test statistic. We illustrate the method using published data on tuberculoid leprosy and HLA. We show that the test procedure is invariant, and extend the method to the case of a two-locus recessive disease.