diff --git a/sphinx/builders/__init__.py b/sphinx/builders/__init__.py
index 9bcc8c7b1eb..ae23556546f 100644
--- a/sphinx/builders/__init__.py
+++ b/sphinx/builders/__init__.py
@@ -314,8 +314,7 @@ def build(
 
         doccount = len(updated_docnames)
         logger.info(bold(__('looking for now-outdated files... ')), nonl=True)
-        for docname in self.env.check_dependents(self.app, updated_docnames):
-            updated_docnames.add(docname)
+        updated_docnames.update(self.env.check_dependents(self.app, updated_docnames))
         outdated = len(updated_docnames) - doccount
         if outdated:
             logger.info(__('%d found'), outdated)