Transfection of the human malaria parasite Plasmodium falciparum is currently performed with circularised plasmids that are maintained episomally in parasites under drug selection but which are rapidly lost when selection pressure is removed. In this paper, we show that in instances where gene targeting is not favoured, transfected plasmids can change to stably replicating forms (SRFs) that are maintained episomally in the absence of drug selection. SRF DNA is a large concatamer of the parental plasmid comprising at least nine plasmids arranged in a head-to-tail array. We show as well that the original unstable replicating forms (URFs) are also present as head-to-tail concatamers, but only comprise three plasmids. Limited digestion and gamma irradiation experiments revealed that while URF concatamers are primarily circular, as expected, SRF concatamers form a more complex structure that includes extensive single-stranded DNA. No evidence of sequence rearrangement or additional sequence was detected in SRF DNA, including in transient replication experiments designed to select for more efficiently replicating plasmids. Surprisingly, these experiments revealed that the bacterial plasmid alone can replicate in parasites. Together, these results imply that transfected plasmids are required to form head-to-tail concatamers to be maintained in parasites and implicate both rolling-circle and recombination-dependent mechanisms in their replication.