Method and system for reducing the number of ports allocated by a relay

A method and system for reducing the number of ports allocated by a relay server is provided. A connection system uses a bidirectional technique to establish a connection via the relay server between two endpoints (e.g., client computers) that can be used bidirectionally to send a stream from a first endpoint to a second endpoint and a stream from the second endpoint to the first endpoint. The connection system may also use a stream multiplexing technique to further reduce the number of ports allocated by a relay server by multiplexing multiple streams onto a single connection. The connection system may also use an endpoint multiplexing technique to reduce the number of ports allocated by a relay server by multiplexing streams from different endpoints through a single connection via the relay server.