In this paper, we investigate the consensus problem for high-order multiple non-holonomic systems, in which the leader's reference input signals are unknown to all the followers. Under the assumption that the leader is the root of a spanning tree, by using the backstepping design method, distributed adaptive controllers are constructed recursively. To assure the stability of the overall scheme, projection techniques are employed to modify the uncertain parameters of the desired trajectory. By using algebraic graph theory and Lyapunov theory, it is shown that all closed-loop signals are bounded, and the followers' states converge to the desired reference trajectory asymptotically. Finally, simulation examples are given to show the effectiveness of the proposed control scheme.