diff --git a/Lib/functools.py b/Lib/functools.py
index 1a1f22e..01889cb 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -53,17 +53,17 @@
 def total_ordering(cls):
     """Class decorator that fills in missing ordering methods"""
     convert = {
-        '__lt__': [('__gt__', lambda self, other: other < self),
-                   ('__le__', lambda self, other: not other < self),
+        '__lt__': [('__gt__', lambda self, other: not (self < other or self == other)),
+                   ('__le__', lambda self, other: self < other or self == other),
                    ('__ge__', lambda self, other: not self < other)],
-        '__le__': [('__ge__', lambda self, other: other <= self),
-                   ('__lt__', lambda self, other: not other <= self),
+        '__le__': [('__ge__', lambda self, other: not self <= other or self == other),
+                   ('__lt__', lambda self, other: self <= other and not self == other),
                    ('__gt__', lambda self, other: not self <= other)],
-        '__gt__': [('__lt__', lambda self, other: other > self),
-                   ('__ge__', lambda self, other: not other > self),
+        '__gt__': [('__lt__', lambda self, other: not (self > other or self == other)),
+                   ('__ge__', lambda self, other: self > other or self == other),
                    ('__le__', lambda self, other: not self > other)],
-        '__ge__': [('__le__', lambda self, other: other >= self),
-                   ('__gt__', lambda self, other: not other >= self),
+        '__ge__': [('__le__', lambda self, other: (not self >= other) or self == other),
+                   ('__gt__', lambda self, other: self >= other and not self == other),
                    ('__lt__', lambda self, other: not self >= other)]
     }
     roots = set(dir(cls)) & set(convert)
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index 6bc7b2b..a713314 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -361,6 +361,8 @@
                 self.value = value
             def __lt__(self, other):
                 return self.value < other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -375,6 +377,8 @@
                 self.value = value
             def __le__(self, other):
                 return self.value <= other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -389,6 +393,8 @@
                 self.value = value
             def __gt__(self, other):
                 return self.value > other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -403,6 +409,8 @@
                 self.value = value
             def __ge__(self, other):
                 return self.value >= other.value
+            def __eq__(self, other):
+                return self.value == other.value
         self.assertTrue(A(1) < A(2))
         self.assertTrue(A(2) > A(1))
         self.assertTrue(A(1) <= A(2))
@@ -428,6 +436,22 @@
             class A:
                 pass
 
+    def test_bug_10042(self):
+        @functools.total_ordering
+        class TestTO:
+            def __init__(self, value):
+                self.value = value
+            def __eq__(self, other):
+                if isinstance(other, TestTO):
+                    return self.value == other.value
+                return False
+            def __lt__(self, other):
+                if isinstance(other, TestTO):
+                    return self.value < other.value
+                raise TypeError
+        with self.assertRaises(TypeError):
+            TestTO(8) <= ()
+
 def test_main(verbose=None):
     test_classes = (
         TestPartial,
diff --git a/Misc/ACKS b/Misc/ACKS
index 5d617da..66ace9a 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -669,6 +669,7 @@
 Steven Reiz
 Roeland Rengelink
 Tim Rice
+Francesco Ricciardi
 Jan Pieter Riegel
 Armin Rigo
 Nicholas Riley
diff --git a/Misc/NEWS b/Misc/NEWS
index 9c136aa..c42d89b 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -43,6 +43,9 @@
 Library
 -------
 
+- Issue #10042: Fixed the total_ordering decorator to handle cross-type
+  comparisons that could lead to infinite recursion.
+
 - Issue #10979: unittest stdout buffering now works with class and module
   setup and teardown.