diff --git a/amaranth/lib/wiring.py b/amaranth/lib/wiring.py
index cc1977b..c8a4287 100644
--- a/amaranth/lib/wiring.py
+++ b/amaranth/lib/wiring.py
@@ -552,7 +552,10 @@ class FlippedInterface:
 
 
 def flipped(interface):
-    return FlippedInterface(interface)
+    if type(interface) is FlippedInterface:
+        return interface._FlippedInterface__unflipped
+    else:
+        return FlippedInterface(interface)
 
 
 @final
diff --git a/tests/test_lib_wiring.py b/tests/test_lib_wiring.py
index 06e9bab..d33ac7e 100644
--- a/tests/test_lib_wiring.py
+++ b/tests/test_lib_wiring.py
@@ -530,6 +530,7 @@ class FlippedInterfaceTestCase(unittest.TestCase):
         self.assertEqual(tintf, flipped(intf))
         self.assertRegex(repr(tintf),
             r"^flipped\(<.+?\.Interface object at .+>\)$")
+        self.assertIs(flipped(tintf), intf)
 
     def test_getattr_setattr(self):
         class I(Interface):