diff --git a/doc/source/whatsnew/v1.4.3.rst b/doc/source/whatsnew/v1.4.3.rst
index ca8b8ca15ec47..bfc9422711690 100644
--- a/doc/source/whatsnew/v1.4.3.rst
+++ b/doc/source/whatsnew/v1.4.3.rst
@@ -20,6 +20,7 @@ Fixed regressions
 - Fixed regression in :func:`read_fwf` raising ``ValueError`` when ``widths`` was specified with ``usecols`` (:issue:`46580`)
 - Fixed regression in :func:`concat` not sorting columns for mixed column names (:issue:`47127`)
 - Fixed regression in :meth:`.Groupby.transform` and :meth:`.Groupby.agg` failing with ``engine="numba"`` when the index was a :class:`MultiIndex` (:issue:`46867`)
+- Fixed regression in ``NaN`` comparison for :class:`Index` operations where the same object was compared (:issue:`47105`)
 - Fixed regression is :meth:`.Styler.to_latex` and :meth:`.Styler.to_html` where ``buf`` failed in combination with ``encoding`` (:issue:`47053`)
 - Fixed regression in :func:`read_csv` with ``index_col=False`` identifying first row as index names when ``header=None`` (:issue:`46955`)
 - Fixed regression in :meth:`.DataFrameGroupBy.agg` when used with list-likes or dict-likes and ``axis=1`` that would give incorrect results; now raises ``NotImplementedError`` (:issue:`46995`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index cb01cfc981739..01bbc424c3764 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -6955,7 +6955,7 @@ def _cmp_method(self, other, op):
                     # TODO: should set MultiIndex._can_hold_na = False?
                     arr[self.isna()] = False
                 return arr
-            elif op in {operator.ne, operator.lt, operator.gt}:
+            elif op is operator.ne:
                 arr = np.zeros(len(self), dtype=bool)
                 if self._can_hold_na and not isinstance(self, ABCMultiIndex):
                     arr[self.isna()] = True
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 943cc945995a1..5d7fc23feb5a8 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -2,6 +2,7 @@
 from datetime import datetime
 from io import StringIO
 import math
+import operator
 import re
 
 import numpy as np
@@ -1604,3 +1605,16 @@ def test_get_attributes_dict_deprecated():
     with tm.assert_produces_warning(DeprecationWarning):
         attrs = idx._get_attributes_dict()
     assert attrs == {"name": None}
+
+
+@pytest.mark.parametrize("op", [operator.lt, operator.gt])
+def test_nan_comparison_same_object(op):
+    # GH#47105
+    idx = Index([np.nan])
+    expected = np.array([False])
+
+    result = op(idx, idx)
+    tm.assert_numpy_array_equal(result, expected)
+
+    result = op(idx, idx.copy())
+    tm.assert_numpy_array_equal(result, expected)