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Abstract Background The genus Musa is a large species complex which includes cultivars at diploid and triploid levels. These sterile and vegetatively propagated cultivars are based on the A genome from Musa acuminata, exclusively for sweet bananas such as Cavendish, or associated with the B genome (Musa balbisiana) in cooking bananas such as Plantain varieties. In M. acuminata cultivars, structural heterozygosity is thought to be one of the main causes of sterility, which is essential for obtaining seedless fruits but hampers breeding. Only partial genetic maps are presently available due to chromosomal rearrangements within the parents of the mapping populations. This causes large segregation distortions inducing pseudo-linkages and difficulties in ordering markers in the linkage groups. The present study aims at producing a saturated linkage map of M. acuminata, taking into account hypotheses on the structural heterozygosity of the parents. Results An F1 progeny of 180 individuals was obtained from a cross between two genetically distant accessions of M. acuminata, 'Borneo' and 'Pisang Lilin' (P. Lilin). Based on the gametic recombination of each parent, two parental maps composed of SSR and DArT markers were established. A significant proportion of the markers (21.7%) deviated (p < 0.05) from the expected Mendelian ratios. These skewed markers were distributed in different linkage groups for each parent. To solve some complex ordering of the markers on linkage groups, we associated tools such as tree-like graphic representations, recombination frequency statistics and cytogenetical studies to identify structural rearrangements and build parsimonious linkage group order. An illustration of such an approach is given for the P. Lilin parent. Conclusions We propose a synthetic map with 11 linkage groups containing 489 markers (167 SSRs and 322 DArTs) covering 1197 cM. This first saturated map is proposed as a "reference Musa map" for further analyses. We also propose two complete parental maps with interpretations of structural rearrangements localized on the linkage groups. The structural heterozygosity in P. Lilin is hypothesized to result from a duplication likely accompanied by an inversion on another chromosome. This paper also illustrates a methodological approach, transferable to other species, to investigate the mapping of structural rearrangements and determine their consequences on marker segregation.