diff --git a/Lib/test/test_shutil.py b/Lib/test/test_shutil.py
index 06ca50a..890f2c7 100644
--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -1849,6 +1849,23 @@ def test_pathext(self):
             rv = shutil.which(program, path=self.temp_dir)
             self.assertEqual(rv, temp_filexyz.name)
 
+    # Issue 40592: See https://bugs.python.org/issue40592
+    @unittest.skipUnless(sys.platform == "win32", 'test specific to Windows')
+    def test_pathext_with_empty_str(self):
+        ext = ".xyz"
+        temp_filexyz = tempfile.NamedTemporaryFile(dir=self.temp_dir,
+                                                   prefix="Tmp2", suffix=ext)
+        self.addCleanup(temp_filexyz.close)
+
+        # strip path and extension
+        program = os.path.basename(temp_filexyz.name)
+        program = os.path.splitext(program)[0]
+
+        with os_helper.EnvironmentVarGuard() as env:
+            env['PATHEXT'] = f"{ext};"  # note the ;
+            rv = shutil.which(program, path=self.temp_dir)
+            self.assertEqual(rv, temp_filexyz.name)
+
 
 class TestWhichBytes(TestWhich):
     def setUp(self):