In Escherichia coli DNA replication yields two interlinked circular chromosomes. Returning the chromosomes to an unlinked monomeric state is essential to cell survival. Simplification of DNA topology is mediated by enzymes, such as recombinases and topoisomerases. Recombinases act by a local reconnection event. We investigate analytically minimal pathways of unlinking by local reconnection. We introduce a Monte Carlo method to simulate local reconnection, provide a quantitative measure to distinguish among pathways and identify a most probable pathway. These results point to a universal property relevant to any local reconnection event between two sites along one or two circles.