A mobile multi-agent system is proposed to create solutions for the university course timetabling problem. It is composed of four kinds of agents: (mobile) Course Agents, and (stationary) Signboard, Publisher and Interface Agents. The key strength of this new approach is to use a fundamental attribute of Agents that of autonomy. This autonomy is manifested in this work in the Course Agent. Each Course Agent in the system is responsible for negotiating with other Course Agents to find satisfactory class resource for the course they represent. This negotiation occurs initially indirectly through a Signboard Agent. A set of rules is used to structure Agent-to-Agent negotiation to find mutually acceptable class resources. The scheduling problem is executed in a natural parallel structure using one Signboard Agent to represent a weekday. The experimental results show that this new approach has merit and can lead to acceptable and flexible solutions to the course timetabling problem.