diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index bd3bee507baa3..f0083ab46d14d 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -378,7 +378,7 @@ Numeric
 Categorical
 ^^^^^^^^^^^
 
--
+- Bug in ``Categorical.equals`` between two unordered categories with the same categories, but in a different order (:issue:`16603`)
 -
 -
 
diff --git a/pandas/core/categorical.py b/pandas/core/categorical.py
index d47cb0762447b..8b86de285b0fe 100644
--- a/pandas/core/categorical.py
+++ b/pandas/core/categorical.py
@@ -2081,8 +2081,16 @@ def equals(self, other):
         -------
         are_equal : boolean
         """
-        return (self.is_dtype_equal(other) and
-                np.array_equal(self._codes, other._codes))
+        if self.is_dtype_equal(other):
+            if self.categories.equals(other.categories):
+                # fastpath to avoid re-coding
+                other_codes = other._codes
+            else:
+                other_codes = _recode_for_categories(other.codes,
+                                                     other.categories,
+                                                     self.categories)
+            return np.array_equal(self._codes, other_codes)
+        return False
 
     def is_dtype_equal(self, other):
         """
diff --git a/pandas/tests/categorical/test_operators.py b/pandas/tests/categorical/test_operators.py
index 09a0607b67a88..fa8bb817616e4 100644
--- a/pandas/tests/categorical/test_operators.py
+++ b/pandas/tests/categorical/test_operators.py
@@ -250,6 +250,13 @@ def test_compare_different_lengths(self):
         with tm.assert_raises_regex(TypeError, msg):
             c1 == c2
 
+    def test_compare_unordered_different_order(self):
+        # https://github.com/pandas-dev/pandas/issues/16603#issuecomment-
+        # 349290078
+        a = pd.Categorical(['a'], categories=['a', 'b'])
+        b = pd.Categorical(['b'], categories=['b', 'a'])
+        assert not a.equals(b)
+
     def test_numeric_like_ops(self):
 
         df = DataFrame({'value': np.random.randint(0, 10000, 100)})
diff --git a/pandas/tests/indexes/test_category.py b/pandas/tests/indexes/test_category.py
index f7328a99195b9..d5c0494df030a 100644
--- a/pandas/tests/indexes/test_category.py
+++ b/pandas/tests/indexes/test_category.py
@@ -747,6 +747,15 @@ def test_equals_categorical(self):
                                               ordered=True))
         assert ci.equals(ci.copy())
 
+    def test_equals_categoridcal_unordered(self):
+        # https://github.com/pandas-dev/pandas/issues/16603
+        a = pd.CategoricalIndex(['A'], categories=['A', 'B'])
+        b = pd.CategoricalIndex(['A'], categories=['B', 'A'])
+        c = pd.CategoricalIndex(['C'], categories=['B', 'A'])
+        assert a.equals(b)
+        assert not a.equals(c)
+        assert not b.equals(c)
+
     def test_string_categorical_index_repr(self):
         # short
         idx = pd.CategoricalIndex(['a', 'bb', 'ccc'])