A genetic map consisting of three loci anchored at the centromere of bovine chromosome 23 was constructed by genotyping secondary oocytes (SO) and first polar bodies (PB1) using a polymerase chain reaction (PCR)-based approach. Primary oocytes arrested in prophase of meiosis I were stimulated in vitro to resume division and extrude PB1. Sixty SO and their matched PB1 were collected from 14 cows by micro-manipulation, subjected to amplification of the whole genome by primer extension preamplification, and genotyped independently for the linked genes PRL, DRB3, and DYA by PCR-RFLP analysis. Single-locus analysis of gene-centromere recombination rates were theta cen-DYA = 0.042, theta cen-DRB3 = 0.113, and theta cen-PRL = 0.166. The most likely order is cen-DYA-DRB3-PRL. Analysis of typing data from 3 cows revealed three meiotic divisions consistent with "linkage phase exchange" between DYA and DRB3 or PRL. One of the three linkage phase exchanges was confirmed by complementary genotypes in a matched secondary oocyte-first polar body pair. Such linkage phase exchanges could result from four-strand double crossovers between homologous chromosomes. Because all four gametes produced by four-strand double crossovers will be recombinant, more frequent occurrence of such events in females may explain the sexual dimorphism in genetic maps. Alternatively, four-strand crossovers could represent a type of recombination hotspot between DYA and DRB3, suggesting a mechanism for the high recombination frequency (15%) between these two class II genes of the bovine major histocompatibility complex.