Although monocotyledonous-plant-infecting mastreviruses (in the family Geminiviridae) are known to cause economically significant crop losses in certain areas of the world, in Australia, they pose no obvious threat to agriculture. Consequently, only a few Australian monocot-infecting mastreviruses have been described, and only two have had their genomes fully sequenced. Here, we present the third full-genome sequence of an Australian monocot-infecting mastrevirus from Bromus catharticus belonging to a distinct species, which we have tentatively named Bromus catharticus striate mosaic virus (BCSMV). Although the genome of this new virus shares only 57.7% sequence similarity with that of its nearest known relative, Digitaria didactyla striate mosaic virus (DDSMV; also from Australia), it has features typical of all other known mastrevirus genomes. Phylogenetic analysis showed that both the full genome and each of its probable expressed proteins group with the two other characterised Australian monocot-infecting mastreviruses. Besides the BCSMV genome sequence revealing that Australian monocot-infecting mastrevirus diversity rivals that seen in Africa, it has enabled us, for the first, to time detect evidence of recombination amongst the Australian viruses. Specifically, it appears that DDSMV possesses a short intergenic region sequence that has been recombinationally derived from either BCSMV or a close relative that has not yet been identified.