Saccharomyces strains with chimerical genomes consisting of mosaics of the genomes of different species ("natural hybrids") occur quite frequently among industrial and wine strains. The most widely endorsed hypothesis is that the mosaics are introgressions acquired via hybridisation and repeated backcrosses of the hybrids with one of the parental species. However, the interspecies hybrids are sterile, unable to mate with their parents. Here, we show by analysing synthetic Saccharomyces kudriavzevii x Saccharomyces uvarum hybrids that mosaic (chimeric) genomes can arise without introgressive backcrosses. These species are biologically separated by a double sterility barrier (sterility of allodiploids and F1 sterility of allotetraploids). F1 sterility is due to the diploidisation of the tetraploid meiosis resulting in MAT a /MAT alpha heterozygosity which suppresses mating in the spores. This barrier can occasionally be broken down by malsegregation of autosyndetically paired chromosomes carrying the MAT loci (loss of MAT heterozygosity). Subsequent malsegregation of additional autosyndetically paired chromosomes and occasional allosyndetic interactions chimerise the hybrid genome. Chromosomes are preferentially lost from the S. kudriavzevii subgenome. The uniparental transmission of the mitochondrial DNA to the hybrids indicates that nucleo-mitochondrial interactions might affect the direction of the genomic changes. We propose the name GARMe (Genome AutoReduction in Meiosis) for this process of genome reduction and chimerisation which involves no introgressive backcrossings. It opens a way to transfer genetic information between species and thus to get one step ahead after hybridisation in the production of yeast strains with beneficial combinations of properties of different species.