The London Urban Traffic Control (UTC) system has been in operation for over 20 years. There are two major systems in operation: fixed time plans and SCOOT. The UTC system controls some 2000 traffic signals in Greater London on a second by second basis over the British Telecom based leased-line data circuits. Timetable algorithms enable a plan to be selected for a given junction or a group of junctions, at different times of the day. In standard timetable algorithms, a text based file stores the times and the corresponding plans and then the required plans are selected at the specified times of the day. In large UTC systems the size of this text file can be very large and difficult to manage. This paper describes a new timetable algorithm which is based on groups and it is shown that this algorithm simplifies the management of timetable operations in large UTC systems. (A*) For the covering abstract see ITRD E110327.