diff --git a/udp_muxed_conn.go b/udp_muxed_conn.go
index ba3297b5..4e6588d0 100644
--- a/udp_muxed_conn.go
+++ b/udp_muxed_conn.go
@@ -77,7 +77,7 @@ func (c *udpMuxedConn) ReadFrom(b []byte) (n int, rAddr net.Addr, err error) {
 
 		if c.state == udpMuxedConnClosed {
 			c.mu.Unlock()
-			return 0, nil, io.ErrClosedPipe
+			return 0, nil, io.EOF
 		}
 
 		c.state = udpMuxedConnWaiting
@@ -86,7 +86,7 @@ func (c *udpMuxedConn) ReadFrom(b []byte) (n int, rAddr net.Addr, err error) {
 		select {
 		case <-c.notify:
 		case <-c.closedChan:
-			return 0, nil, io.ErrClosedPipe
+			return 0, nil, io.EOF
 		}
 	}
 }