diff --git a/src/mux_h1.c b/src/mux_h1.c
index f9048b1..b1eebf1 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -1184,7 +1184,9 @@
 
 	TRACE_ENTER(H1_EV_RX_DATA|H1_EV_RX_HDRS, h1s->h1c->conn, h1s,, (size_t[]){max});
 
-	if (!(h1s->flags & H1S_F_NOT_FIRST) && !(h1m->flags & H1_MF_RESP)) {
+	if (!(h1s->h1c->px->options2 & PR_O2_NO_H2_UPGRADE) && /* H2 upgrade supported by the proxy */
+	    !(h1s->flags & H1S_F_NOT_FIRST) &&                 /* It is the first transaction */
+	    !(h1m->flags & H1_MF_RESP)) {                      /* It is a request */
 		/* 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) {