diff --git a/zerver/tests/test_users.py b/zerver/tests/test_users.py
index fa61ab4b3c..9b2a62a5a2 100644
--- a/zerver/tests/test_users.py
+++ b/zerver/tests/test_users.py
@@ -173,6 +173,9 @@ class PermissionTest(ZulipTestCase):
         self.assert_json_success(result)
         hamlet = self.example_user('hamlet')
         self.assertEqual(hamlet.full_name, new_name)
+        req['is_admin'] = ujson.dumps(False)
+        result = self.client_patch('/json/users/{}'.format(hamlet.id), req)
+        self.assert_json_success(result)
 
     def test_non_admin_cannot_change_full_name(self) -> None:
         self.login(self.example_email("hamlet"))
diff --git a/zerver/views/users.py b/zerver/views/users.py
index ea7d0199f8..26ccbabd7e 100644
--- a/zerver/views/users.py
+++ b/zerver/views/users.py
@@ -81,7 +81,7 @@ def update_user_backend(request: HttpRequest, user_profile: UserProfile, user_id
                         is_admin: Optional[bool]=REQ(default=None, validator=check_bool)) -> HttpResponse:
     target = access_user_by_id(user_profile, user_id, allow_deactivated=True, allow_bots=True)
 
-    if is_admin is not None:
+    if is_admin is not None and target.is_realm_admin != is_admin:
         if not is_admin and check_last_admin(user_profile):
             return json_error(_('Cannot remove the only organization administrator'))
         do_change_is_admin(target, is_admin)