Strong social relationships confer health and fitness benefits in a number of species, motivating the need to understand the processes through which they arise. In female cercopithecine primates, both kinship and dominance rank are thought to influence rates of affiliative behaviour and social partner preference. Teasing apart the relative importance of these factors has been challenging, however, as female kin often occupy similar positions in the dominance hierarchy. Here, we isolated the specific effects of rank on social relationships in female rhesus macaques by analysing grooming patterns in 18 social groups that did not contain close relatives, and in which dominance ranks were experimentally randomized. We found that grooming was asymmetrically directed towards higher-ranking females and that grooming bouts temporarily decreased the likelihood of aggression between grooming partners, supporting the idea that grooming is associated with social tolerance. Even in the absence of kin, females formed the strongest grooming relationships with females adjacent to them in rank, a pattern that was strongest for the highest-ranking females. Using simulations, we show that three rules for allocating grooming based on dominance rank recapitulated most of the relationships we observed. Finally, we evaluated whether a female's tendency to engage in grooming behaviour was stable across time and social setting. We found that one measure, the rate of grooming females provided to others (but not the rate of grooming females received), exhibited modest stability after accounting for the primary effect of dominance rank. Together, our findings indicate that dominance rank has strong effects on social relationships in the absence of kin, suggesting the importance of considering social status and social connectedness jointly when investigating their health and fitness consequences.