diff --git a/src/mux_h2.c b/src/mux_h2.c
index c56efc2..bfcfc26 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -4602,7 +4602,7 @@
 	}
 
 	if (htx) {
-		while (count && !htx_is_empty(htx)) {
+		while (!(h2s->flags & H2_SF_BLK_ANY) && count && !htx_is_empty(htx)) {
 			idx   = htx_get_head(htx);
 			blk   = htx_get_blk(htx, idx);
 			btype = htx_get_blk_type(blk);