The terminal structures of the Borna disease virus (BDV) genome (vRNA) and antigenome (cRNA) differ from those of other negative strand RNA viruses, as both molecules possess four nucleotides at the 3' terminus without an apparent template at the 5' end of the opposite strand. Consequently, the v- and cRNA molecules are not perfect mirror images, a situation that is not compatible with conventional strategies to maintain genetic information. We show here that recombinant viruses recovered from cDNA lacking the nontemplated nucleotides efficiently reconstitute the 3' overhangs. Analyses of recombinant viruses encoding genetic markers in potential alternative template sequences demonstrated that the BDV v- and cRNA molecules are extended by a realign-and-elongation process on internal template motifs located in close proximity to the 3' ends of v- and cRNA, respectively. The data further suggest that cRNA elongation is restricted to a single template motif of the nascent strand, whereas elongation of vRNA might use multiple template motifs. We propose that the elongation of the 3' termini supports the terminal integrity of the genomic RNA molecules during BDV persistence, and furthermore provides an elegant strategy to eliminate the triphosphate groups from the 5' termini of the BDV v- and cRNA without compromising the genetic information of the virus.