The Mirndi language family is one of the very few discontinuous language families that have been proposed for Australia. This reconstruction shows that there is a sufficient evidentiary basis, according to the canons of standard historical linguistics, to show that the Mirndi languages constitute a distinct language family. The evidence comes from closed class morphemes, both grammatical and lexical. The evidence from open, lexical classes is negligible and would not suffice to establish the family. The reconstruction also considers the evidence as to the territorial associations of Proto-Mirndi. There are a number of strands of evidence, which though limited, all converge in indicating that the territorial associations of Proto-Mirndi were in the vicinity of the south-western Gulf of Carpentaria. As such, this implies shifts in territorial affiliations of the Mirndi varieties from east to west. In addition its linguistic aspects, the reconstruction also provides a detailed overview of the history of subsections. Subsections are a salient social construct across much of north-central and north-western Australia. The reconstruction shows that subsections are of considerable time depth, and also that the diffusion of subsections is of considerable time depth.