In allopolyploids, correct chromosome segregation requires suppression of non-homologous crossovers while levels of homologous crossovers are ensured. To date, no mechanism able to specifically inhibit non-homologous crossovers has been described in allopolyploids other than in bread wheat. Here, we show that reducing the number of functional copies of MSH4, an essential gene for the main crossover pathway, prevents non-homologous crossovers in allotetraploid Brassica napus. We show that non-homologous crossovers originate almost exclusively from the MSH4-dependent recombination pathway and that their numbers decrease when MSH4 returns to single copy in B. napus; by contrast, homologous crossovers remain unaffected by MSH4 duplicate loss. We also demonstrate that MSH4 systematically returns to single copy following numerous independent polyploidy events, a pattern that is probably not by chance. These results suggest that stabilization of allopolyploid meiosis can be enhanced by loss of a key meiotic recombination gene.