The ABR service class provides feedback based traffic control to transport bursty data traffic efficiently. Feedback based congestion control has first been studied to be applied to unicast connections. Recently. several congestion control algorithms for multicast connections have also been proposed as the number of ABR applications requiring multicast increases. With feedback based congestion control, the effectiveness of a traffic control scheme diminishes as propagation delay increases. Especially for a multicast connection, a remote destination may suffer unfair service compared to a local destination due to the delayed feedback. Amelioration of the disadvantages caused by feedback delay is therefore more important for remote destinations in multicast connections. This paper proposes a new switch behavior to provide effective feedback based mathc control for rentoh destinations. The proposed switches adjust the service rate dynamically in accordance woth the state of the downstream, that is, the congestion of the destinaion is immediately controlled by the nearest apstream switch before the source to ramp down the transmission rate of the connection. The proposed switch has an implementation overhead to have a separate buffer for each VC to adjust the service rate in accordance with a backward Rm cell of each VC. The buffer requirement id also increased at intermediate switches. Simulation results show that the proposed switch reduces the cell loss rate in both the local and the remote destinations and slso amelioratd the between the two destinations.