diff --git a/Lib/test/test_exceptions.py b/Lib/test/test_exceptions.py
index 289288478c285a..075b1c41ff3d7f 100644
--- a/Lib/test/test_exceptions.py
+++ b/Lib/test/test_exceptions.py
@@ -1840,7 +1840,13 @@ def f():
             with support.captured_stderr() as err:
                 sys.__excepthook__(*sys.exc_info())
 
-        self.assertNotIn("a1", err.getvalue())
+        traceback = err.getvalue()
+
+        # remvoe the source path from the traceback, it could contain "a1" in it
+        # https://bugs.python.org/issue45400
+        traceback = traceback.replace(__file__, os.path.basename(__file__))
+
+        self.assertNotIn("a1", traceback)
 
     def test_name_error_with_custom_exceptions(self):
         def f():
diff --git a/Misc/NEWS.d/next/Tests/2021-10-07-13-17-42.bpo-45400.oHgprZ.rst b/Misc/NEWS.d/next/Tests/2021-10-07-13-17-42.bpo-45400.oHgprZ.rst
new file mode 100644
index 00000000000000..ac586d7a0050ac
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2021-10-07-13-17-42.bpo-45400.oHgprZ.rst
@@ -0,0 +1,4 @@
+The ``test_name_error_suggestions_do_not_trigger_for_too_many_locals`` will
+no longer fail when run from a directory that contains ``a1`` in the path,
+which is likely to happen when building from unpacked sources of a first
+alpha release.