In various social species, animals have been observed to share friendly relationships with some group members and to resolve conflicts through reconciliation, the exchange of affiliative behaviour soon after a conflict that functions to restore the relationship between the former opponents. The valuable relationship hypothesis predicts that reconciliation should be observed more often after conflicts between friends. Friendly relationships can be described by three dimensions (i.e. value, security and compatibility); however, research into the relative importance of these dimensions for the occurrence of reconciliation is sparse. Moreover, reconciliation may depend on factors other than the social relationship between opponents including, for example, their social status or the context of the conflict. Our study aimed at analysing which factors are important determinants of reconciliation and at testing the valuable relationship hypothesis, by analysing the relative effects of relationship value, security and compatibility on the occurrence and timing of reconciliation. We collected data on two troops of wild Japanese macaques living on Yakushima Island, Japan, and selected the best predicting variables of reconciliation using linear mixed models. Our results show that reconciliation occurs more frequently, and earlier, after conflicts between opponents who exchange a higher percentage of grooming. Two additional variables related to relationship security and value were selected in the best models: frequency of aggression and of approaches resulting in tolerated co-feeding. Among the variables not related to relationship quality, distance between opponents at the end of the conflict, kinship, sex of the opponents and context of conflict (i.e. during feeding or social time) were included in our models. Our findings support the valuable relationship hypothesis and, in particular, highlight that the fitness-related benefits of social relationships (i.e. the relationship value) are important determinants of the evolution of friendly relationships and reconciliation.