The protozoan parasite Giardia intestinalis (also known as Giardia lamblia) is a major waterborne pathogen. During its life cycle, Giardia alternates between the actively growing trophozoite, which has two diploid nuclei with low levels of allelic heterozygosity, and the infectious cyst, which has four nuclei and a tough outer wall. Although the formation of the cyst wall has been studied extensively, we still lack basic knowledge about many fundamental aspects of the cyst, including the sources of the four nuclei and their distribution during the transformation from cyst into trophozoite. In this study, we tracked the identities of the nuclei in the trophozoite and cyst using integrated nuclear markers and immunofluorescence staining. We demonstrate that the cyst is formed from a single trophozoite by a mitotic division without cytokinesis and not by the fusion of two trophozoites. During excystation, the cell completes cytokinesis to form two daughter trophozoites. The non-identical nuclear pairs derived from the parent trophozoite remain associated in the cyst and are distributed to daughter cells during excystation as pairs. Thus, nuclear sorting (such that each daughter cell receives a pair of identical nuclei) does not appear to be a mechanism by which Giardia reduces heterozygosity between its nuclei. Rather, we show that the cyst nuclei exchange chromosomal genetic material, perhaps as a way to reduce heterozygosity in the absence of meiosis and sex, which have not been described in Giardia. These results shed light on fundamental aspects of the Giardia life cycle and have implications for our understanding of the population genetics and cell biology of this binucleate parasite.