diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 68c1839221508..6d5e40d37c8df 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -91,7 +91,7 @@ Categorical
 Datetimelike
 ^^^^^^^^^^^^
 
--
+- Fixed bug where two :class:`DateOffset` objects with different ``normalize`` attributes could evaluate as equal (:issue:`21404`)
 -
 -
 
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index 8bf0d9f915d04..6fd525f02f55c 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -564,11 +564,10 @@ def setup_method(self, method):
         self.offset2 = BDay(2)
 
     def test_different_normalize_equals(self):
-        # equivalent in this special case
-        offset = BDay()
-        offset2 = BDay()
-        offset2.normalize = True
-        assert offset == offset2
+        # GH#21404 changed __eq__ to return False when `normalize` doesnt match
+        offset = self._offset()
+        offset2 = self._offset(normalize=True)
+        assert offset != offset2
 
     def test_repr(self):
         assert repr(self.offset) == '<BusinessDay>'
@@ -734,11 +733,10 @@ def test_constructor_errors(self):
             BusinessHour(start='14:00:05')
 
     def test_different_normalize_equals(self):
-        # equivalent in this special case
+        # GH#21404 changed __eq__ to return False when `normalize` doesnt match
         offset = self._offset()
-        offset2 = self._offset()
-        offset2.normalize = True
-        assert offset == offset2
+        offset2 = self._offset(normalize=True)
+        assert offset != offset2
 
     def test_repr(self):
         assert repr(self.offset1) == '<BusinessHour: BH=09:00-17:00>'
@@ -1397,11 +1395,10 @@ def test_constructor_errors(self):
             CustomBusinessHour(start='14:00:05')
 
     def test_different_normalize_equals(self):
-        # equivalent in this special case
+        # GH#21404 changed __eq__ to return False when `normalize` doesnt match
         offset = self._offset()
-        offset2 = self._offset()
-        offset2.normalize = True
-        assert offset == offset2
+        offset2 = self._offset(normalize=True)
+        assert offset != offset2
 
     def test_repr(self):
         assert repr(self.offset1) == '<CustomBusinessHour: CBH=09:00-17:00>'
@@ -1627,11 +1624,10 @@ def setup_method(self, method):
         self.offset2 = CDay(2)
 
     def test_different_normalize_equals(self):
-        # equivalent in this special case
-        offset = CDay()
-        offset2 = CDay()
-        offset2.normalize = True
-        assert offset == offset2
+        # GH#21404 changed __eq__ to return False when `normalize` doesnt match
+        offset = self._offset()
+        offset2 = self._offset(normalize=True)
+        assert offset != offset2
 
     def test_repr(self):
         assert repr(self.offset) == '<CustomBusinessDay>'
@@ -1865,11 +1861,10 @@ class TestCustomBusinessMonthEnd(CustomBusinessMonthBase, Base):
     _offset = CBMonthEnd
 
     def test_different_normalize_equals(self):
-        # equivalent in this special case
-        offset = CBMonthEnd()
-        offset2 = CBMonthEnd()
-        offset2.normalize = True
-        assert offset == offset2
+        # GH#21404 changed __eq__ to return False when `normalize` doesnt match
+        offset = self._offset()
+        offset2 = self._offset(normalize=True)
+        assert offset != offset2
 
     def test_repr(self):
         assert repr(self.offset) == '<CustomBusinessMonthEnd>'
@@ -1982,11 +1977,10 @@ class TestCustomBusinessMonthBegin(CustomBusinessMonthBase, Base):
     _offset = CBMonthBegin
 
     def test_different_normalize_equals(self):
-        # equivalent in this special case
-        offset = CBMonthBegin()
-        offset2 = CBMonthBegin()
-        offset2.normalize = True
-        assert offset == offset2
+        # GH#21404 changed __eq__ to return False when `normalize` doesnt match
+        offset = self._offset()
+        offset2 = self._offset(normalize=True)
+        assert offset != offset2
 
     def test_repr(self):
         assert repr(self.offset) == '<CustomBusinessMonthBegin>'
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index a5a983bf94bb8..99f97d8fc7bc0 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -290,7 +290,7 @@ def _params(self):
         all_paras = self.__dict__.copy()
         if 'holidays' in all_paras and not all_paras['holidays']:
             all_paras.pop('holidays')
-        exclude = ['kwds', 'name', 'normalize', 'calendar']
+        exclude = ['kwds', 'name', 'calendar']
         attrs = [(k, v) for k, v in all_paras.items()
                  if (k not in exclude) and (k[0] != '_')]
         attrs = sorted(set(attrs))