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When the circulatory roadway of a roundabout has more than two lanes, the vehicles' weaving and merging cause large traffic and safety problems. In this paper, a new method of traffic-signal control for modern roundabouts is proposed to solve problems by eliminating the conflict points and weaving sections at a roundabout with different traffic-flow rates on each approach, which normally appear in the real world. A second stop line is set exclusively for the left-turn traffic on the circulatory roadway. It is beside the first stop line on the approach. Traffic signals are installed before each stop line to eliminate the conflicts between the traffic flows on the approaches and the left-turn traffic flows on the circulatory roadway. Left-turn vehicles on the circulatory roadway will stop before red signals to avoid weaving. Equations are derived to compute the signal cycle length and the green time for each traffic flow, considering the limited queue on the circulatory roadway. Capacity and delay are also formulated to evaluate the roundabout's performance. This traffic-signal control has a successful application of a roundabout in Xiamen, China, to solve the very serious traffic-congestion problem. The signal-timing scheme was computed with the proposed equations, as well as the capacity and delay. Pictures taken before and after the improvement show the operation. After the improvement, the roundabout capacity increases 72.1% and the average delay of each vehicle decreases by 20 s.