Factor-mediated reprogramming of somatic cells towards pluripotency is a low-efficiency process during which only small subsets of cells are successfully reprogrammed. Previous analyses of the determinants of the reprogramming potential are based on average measurements across a large population of cells or on monitoring a relatively small number of single cells with live imaging. Here, we applied lentiviral genetic barcoding, a powerful tool enabling the identification of familiar relationships in thousands of cells. High-throughput sequencing of barcodes from successfully reprogrammed cells revealed a significant number of barcodes from related cells. We developed a computer model, according to which a probability of synchronous reprogramming of sister cells equals 10-30%. We conclude that the reprogramming success is pre-established in some particular cells and, being a heritable trait, can be maintained through cell division. Thus, reprogramming progresses in a deterministic manner, at least at the level of cell lineages.