diff --git a/src/mux_h2.c b/src/mux_h2.c
index 1cd76fd..6403b02 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -796,6 +796,7 @@
 	if (!cs)
 		goto out_close;
 
+	cs->flags |= CS_FL_NOT_FIRST;
 	h2s->cs = cs;
 	cs->ctx = h2s;
 	h2c->nb_cs++;