Interpersonal postural coordination (IPC) produced by interpersonal light touch (ILT), whereby time-series variations in the postural sway between two people unintentionally resemble each other, may be a possible social interaction. From a sociopsychological standpoint, close mutual behavioral coordination is recognized as “social glue,” which represents the closeness of relationships and contributes to the building of a good rapport. Therefore, we hypothesized that if IPC functions as social glue, then IPC produced by ILT also represents a social relationship. Participants were dyadic pairs with a preexisting social relationship (acquaintance, friend, or best-friend), and we assessed the closeness between the partners. Postural sway in two quiet standing conditions—no touch (NT) and ILT (a mutual light touch with <1 N) condition—was concurrently measured with the side-by-side standing position, and the association of IPC with intradyadic closeness (rapport) was analyzed using hierarchical linear modeling. The results showed that unintentional IPC was higher in both axes of the ILT condition than in NT condition. Additionally, IPC in the mediolateral axis (the partner side) of the ILT condition was positively correlated with intradyadic closeness, whereas that in the anteroposterior axis (the non-partner side) showed a negative association. As expected, IPC represented intradyadic closeness (rapport). Results indicate that, in unintentional IPC produced by ILT, the priority of processing sensory feedback for postural control, which is received from the individual and a partner, is modulated depending on the rapport in interactional coupled feedback loops between the two individuals (i.e., good rapport increases the degree of taking in feedback from a partner). Thus, unintentional IPC produced by ILT functions as social glue, and it provides an understanding of the sociopsychological aspect in the human-to-human postural coordination mechanism.