diff --git a/src/mux_h1.c b/src/mux_h1.c
index ee12686bb..5056fa88f 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -891,7 +891,7 @@ static size_t h1_process_headers(struct h1s *h1s, struct h1m *h1m, struct htx *h
 	union h1_sl h1sl;
 	int ret = 0;
 
-	if (!(h1m->flags & H1_MF_RESP)) {
+	if (!(h1s->flags & H1S_F_NOT_FIRST) && !(h1m->flags & H1_MF_RESP)) {
 		/* Try to match H2 preface before parsing the request headers. */
 		ret = b_isteq(buf, 0, b_data(buf), ist(H2_CONN_PREFACE));
 		if (ret > 0)