Transit assignment procedures need to reflect the constraints imposed by line routes and timetables. They require specific search algorithms that consider transfers between transit lines with their precise transfer times. Such an assignment procedure is presented for transit networks using a timetable-based search algorithm. In contrast to existing timetable-based search methods employing a shortest-path algorithm, the described procedure constructs connections using branch and bound techniques. This approach significantly reduces computing time, thus facilitating the use of timetable-based assignment for large networks. At the same time, it produces better results in cases where slow but cheap or direct connections compete with fast connections that are more expensive or require transfers.