The coalescent is a sample-based population genetic theory, which is very powerful to understand nucleotide polymorphism patterns within a species. The coalescent was originally developed for eukaryotes, which basically follow vertical inheritance from parents to descendants. Under the framework of the coalescent, we consider the ancestral lineages of a sample backward in time until all sampled sequences reach their most recent common ancestor (MRCA). However, this logic does not hold in bacteria, which often integrate DNAs from external sources (possibly different species) through horizontal gene transfer. One of the outcomes of such integration of an external DNA is that it is exchanged with a homologous part of the recipient genome by homologous recombination. We develop a coalescent theory that incorporates homologous recombination with external sources. When tracing the ancestral lineages of the sampled sequence, if one lineage experienced a homologous recombination from a different species, its ancestral lineage should move to the donor species, implying that it is totally infeasible because any species can be a potential donor. By introducing the novel concept, the most recent external ancestor (MREA), we can construct the ancestral coalescent pattern without considering populations of different species. The theory is readily applied to the analysis of DNA polymorphism data in bacteria.