This paper addresses the problem of how to coordinate the spatial motion of individual agents in a multi-agent system in such a way that the distance between any two agents is maintained at a constant value (but not stabilized) throughout the evolution of the system while simultaneously rotating the formation of agents to a pre-set reference attitude. We propose a distributed control law based on locally available information. The stability of the proposed control law is analyzed using Lyapunov theory in the special case of three agents. The region of attraction is found to encompass the entire statespace, save a single point. A generalization to the case of n agents is performed using the theory of rigid graphs. The geometric underpinnings of these ideas are illustrated by simulation.