In the existing works on multiagent systems with neural-network-based protocols, it is usually assumed that states of all agents are within a compact set so that the approximation accuracy can be guaranteed. However, such an assumption means these protocols may only work if the agents' initial state values are set within a small enough neighborhood of the origin. This article develops a novel neural-network-based consensus protocol for a class of nonlinear multiagent systems. It is strictly proven that the state of each agent is constrained in a solvable compact set for arbitrary initial condition. By introducing the method of designing an internal plant for each agent, the interaction terms of nonlinearities are avoided in the consensus analysis, and the problem of solving the compact set is much simplified. It is also noted that the implementation of the protocol relies on only local interactions of agents' real states, instead of internal plant states. Integrating the adaptive and nonsmooth control techniques, the negative effect from approximation errors can be eliminated and the complete consensus can be reached.