Malaria parasites undergo a single phase of sexual reproduction in their complex lifecycle, during which they cycle between mosquito and vertebrate hosts. Sexual reproduction occurs only at the point when parasites move into the mosquito host. It involves specialised, sexually committed cells called gametocytes, which develop very rapidly into mature gametes and then mate inside the mosquito midgut. The gamete development process is unique, involving unprecedentedly fast replication and cell division to produce male gametes. A single male gametocyte replicates its ~23Mb genome three times over to produce 8 genomes, segregates these into newly-assembled flagellated gamete cells and releases them to seek out female gametes, all within ~15 minutes. Here, for the first time, we use fluorescent labelling of de novo DNA synthesis to follow this process at the whole-cell and single-molecule levels, yielding several novel observations. Firstly, we confirm that no DNA replication occurs before gametogenesis is triggered, although the origin recognition complex protein Orc1 is abundant even in immature gametocytes. Secondly, between repeated rounds of DNA replication there is no detectable karyokinesis - in contrast to the repeated replicative rounds that occur in asexual schizonts. Thirdly, cytokinesis is clearly uncoupled from DNA replication, and can occur even if replication fails, implying a lack of cell cycle checkpoints. Finally the single-molecule dynamics of DNA replication are entirely different from those in asexual schizonts.