python
diff --git a/Lib/test/test_xml_etree.py b/Lib/test/test_xml_etree.py
@@ -3352,6 +3352,37 @@ def test_find_xpath(self):
         self.assertRaisesRegex(SyntaxError, 'XPath', e.find, './tag[last()-0]')
         self.assertRaisesRegex(SyntaxError, 'XPath', e.find, './tag[last()+1]')
 
+    def test_find_xpath_index_no_quadratic_complexity(self):
+        class CountingElement(ET.Element):
+            findall_calls = 0
+            def findall(self, *args, **kwargs):
+                type(self).findall_calls += 1
+                return super().findall(*args, **kwargs)
+
+        def work(n, pattern):
+            root = CountingElement("root")
+            for _ in range(n):
+                ET.SubElement(root, "a")
+            CountingElement.findall_calls = 0
+            root.findall(pattern)
+            return CountingElement.findall_calls
+
+        for pattern in [".//a[1]", ".//a[last()]"]:
+            w1 = work(1024, pattern)
+            w2 = work(2048, pattern)
+            w3 = work(4096, pattern)
+
+            self.assertGreater(w1, 0)
+            r1 = w2 / w1
+            r2 = w3 / w2
+            # Doubling N must not ~double the parent.findall calls.
+            # Linear-in-N call counts indicate the cache is missing.
+            self.assertLess(
+                max(r1, r2), 1.5,
+                msg=f"Possible quadratic behavior on {pattern!r}: "
+                    f"calls={w1, w2, w3} ratios={r1, r2}",
+            )
+
     def test_findall(self):
         e = ET.XML(SAMPLE_XML)
         e[2] = ET.XML(SAMPLE_SECTION)

diff --git a/Lib/xml/etree/ElementPath.py b/Lib/xml/etree/ElementPath.py
@@ -324,15 +324,22 @@ def select_negated(context, result):
                 index = -1
         def select(context, result):
             parent_map = get_parent_map(context)
+            cache = {}
             for elem in result:
                 try:
                     parent = parent_map[elem]
+                except KeyError:
+                    continue
+                key = (parent, elem.tag)
+                if key not in cache:
                     # FIXME: what if the selector is "*" ?
-                    elems = list(parent.findall(elem.tag))
-                    if elems[index] is elem:
-                        yield elem
-                except (IndexError, KeyError):
-                    pass
+                    elems = parent.findall(elem.tag)
+                    try:
+                        cache[key] = elems[index]
+                    except IndexError:
+                        cache[key] = None
+                if cache[key] is elem:
+                    yield elem
         return select
     raise SyntaxError("invalid predicate")
 

diff --git a/Misc/NEWS.d/next/Security/2026-06-30-13-24-13.gh-issue-152674.-2QVoL.rst b/Misc/NEWS.d/next/Security/2026-06-30-13-24-13.gh-issue-152674.-2QVoL.rst
@@ -0,0 +1,6 @@
+The :class:`xml.etree.ElementTree.Element` methods
+:meth:`~xml.etree.ElementTree.Element.findall`,
+:meth:`~xml.etree.ElementTree.Element.iterfind` and
+:meth:`~xml.etree.ElementTree.Element.find` avoid quadratic behavior when
+using XPath index predicates (``[1]``, ``[last()]``, ``[last()-N]``) on XML
+documents with many same-tag siblings.