Final answer:
Homologous recombination is an error-free DNA repair mechanism that repairs double-stranded breaks after DNA replication using the sister chromatid as a template.
Step-by-step explanation:
The error-free DNA repair mechanism known for repairing double-stranded breaks occurring after DNA replication is completed is homologous recombination. This mechanism utilizes the sister chromatid as a template for accurate repair. The process involves several enzymes and proteins, such as MRX, MRN, Sae2, and Sgs1, which play roles in binding at the double-stranded break, recruiting other factors, and facilitating the repair process. Unlike non-homologous end-joining, which can result in deletions, homologous recombination ensures the integrity of the genetic information is maintained without any loss.