Colour polymorphism is known to facilitate speciation but the genetic basis of animal pigmentation and how colour polymorphisms contribute to speciation is poorly understood. Restricted recombination may promote linkage disequilibrium between the colour locus and incompatibility genes. Genomic rearrangement and the position of relevant loci within a chromosome are important factors that influence the frequency of recombination. Therefore, it is important to know the position of the colour locus, gene order and recombination landscape of the chromosome to understand the mechanism that generates incompatibilities between morphs. Recent studies showed remarkable pre- and postzygotic incompatibilities between sympatric colour morphs of the Gouldian finch (Erythrura gouldiae), in which head feather colour is genetically determined by a single sex-linked locus, Red. We constructed a genetic map for the Z chromosome of the Gouldian finch (male-specific map distance=131 cM), using 618 captive-bred birds and 34 microsatellite markers, to investigate the extent of inter- and intraspecific genomic rearrangements and variation in recombination rate within the Z chromosome. We refined the location of the Red locus to a ~7.2-cM interval in a region with a moderate recombination rate but outside the least-recombining, putative centromeric region. There was no evidence of chromosome-wide genomic rearrangements between the chromosomes carrying the red or black alleles with the current marker resolution. This work will contribute to identifying the causal gene, which will in turn enable alternative explanations for the association between incompatibility and colouration, such as fine-scale linkage disequilibrium, genomic rearrangements and pleiotropy, to be tested.