diff --git a/CHANGES.rst b/CHANGES.rst
index 99e1c9bf89f..50919fe907d 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -17,6 +17,7 @@ Bugs fixed
 ----------
 
 * #13392: Fix argument type for ``jieba.load_userdict()``.
+* #13402: Ensure inline ``<script>`` tags are written exactly once.
 
 Testing
 -------
diff --git a/sphinx/application.py b/sphinx/application.py
index ecc636cb37f..fe0e8bdf195 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -1507,6 +1507,7 @@ def add_js_file(
         elif loading_method == 'defer':
             kwargs['defer'] = 'defer'
 
+        filename = filename or ''
         self.registry.add_js_file(filename, priority=priority, **kwargs)
         with contextlib.suppress(AttributeError):
             self.builder.add_js_file(  # type: ignore[attr-defined]