In this paper we propose a modification of the explicit congestion notification (ECN) to correct the bias against connections with long round trip times (RTT) of TCP. The new-ECN algorithm achieves a fair sharing of the available bandwidth of a bottleneck gateway. The idea is to prevent a fast connection from opening its congestion window too quickly and to enable a slow connection to open its window more aggressively. This is done by modifying not only the congestion window size but also by modifying its rate of increase. Both are reduced while receiving marked packets and are increased during times of no congestion. We demonstrate the effect and performance of the new-ECN algorithm with the network simulator "ns" for different network topologies. Additionally, we study the TCP and ECN-TCP friendliness of the new-ECN algorithm. In this paper we only focus on the single bottleneck case. The behavior of new-ECN with multiple congested gateways needs further research.