This work follows from a research project, in which we investigate the underlying mechanisms of human imitation and develop a neural model of its core neural circuits. The present paper presents a model of a neural mechanism by which an imitator agent can map movements of the end effector performed by other agents onto its own frame of reference. The model mechanism is validated in simulation and in a humanoid robot to perform a simple task, in which the robot imitates movements performed a human demonstrator.