We have increased the density of genetic markers on the Arabidopsis lyrata chromosomes AL6 and AL7 corresponding to the A. thaliana chromosome IV, in order to determine chromosome rearrangements between these two species, and to compare recombination fractions across the same intervals. We confirm the two rearrangements previously inferred (a reciprocal translocation and a large inversion, which we infer to be pericentric). By including markers around the centromere regions of A. thaliana chromosomes IV and V, we localize the AL6 centromere, and can localize the breakpoints of these chromosome rearrangements more precisely than previously. One translocation breakpoint was close to the centromere, and the other coincided with one end of the inversion, suggesting that a single event caused both rearrangements. At the resolution of our mapping, apart from these rearrangements, all other markers are in the same order in A. lyrata and A. thaliana. We could thus compare recombination rates in the two species. We found slightly higher values in A. thaliana, and a minimum estimate for regions not close to a centromere in A. lyrata is 4-5 centimorgans per megabase. The mapped region of AL7 includes the self-incompatibility loci (S-loci), and this region has been predicted to have lower recombination than elsewhere in the genome. We mapped 17 markers in a region of 1.23 Mb surrounding these loci, and compared the approximately 600 kb closest to the S-loci with the surrounding region of approximately the same size. There were significantly fewer recombination events in the closer than the more distant region, supporting the above prediction, but showing that the low recombination region is very limited in size.