Binary fission. Binary fission (division in half) is a kind of asexual reproduction. It is the most common form of reproduction in prokaryotes and occurs in some single-celled eukaryotes like Amoeba and Paramecium. In binary fission , the fully grown parent cell splits into two halves , producing two new cells. After replicating its genetic material, the cell divides into two nearly equal sized daughter cells. The genetic material is also equally split.