diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index fe047b4a141ef..4544daf063197 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -273,7 +273,7 @@ Datetimelike
 Timedelta
 ^^^^^^^^^
 
--
+- Bug when :meth:`TimedeltaIndex.intersection` with another decreasing TimedeltaIndex (:issue:`17391`)
 -
 -
 
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index c3ed26b5b1cca..ecf0e0a0cc3e3 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -16,6 +16,7 @@
 from pandas.core.dtypes.missing import isna
 
 from pandas.core.accessor import delegate_names
+from pandas.core.algorithms import unique1d
 from pandas.core.arrays import datetimelike as dtl
 from pandas.core.arrays.timedeltas import TimedeltaArray, _is_convertible_to_td
 from pandas.core.base import _shared_docs
@@ -474,21 +475,34 @@ def intersection(self, other):
             return self
         if len(other) == 0:
             return other
-        # to make our life easier, "sort" the two ranges
-        if self[0] <= other[0]:
-            left, right = self, other
-        else:
-            left, right = other, self
 
-        end = min(left[-1], right[-1])
-        start = right[0]
+        if self.is_monotonic:
+            other = other.sort_values()
+            # to make our life easier, "sort" the two ranges
+            if self[0] <= other[0]:
+                left, right = self, other
+            else:
+                left, right = other, self
 
-        if end < start:
-            return type(self)(data=[])
-        else:
-            lslice = slice(*left.slice_locs(start, end))
-            left_chunk = left.values[lslice]
-            return self._shallow_copy(left_chunk)
+            end = min(left[-1], right[-1])
+            start = right[0]
+
+            if end < start:
+                return type(self)(data=[])
+            else:
+                lstart, lend = left.slice_locs(start, end)
+                lslice = np.arange(lstart, lend)
+                mask = [left_elem in right for left_elem in left[lstart: lend]]
+                lslice = lslice[mask]
+                left_chunk = left.values[lslice]
+                return self._shallow_copy(left_chunk)
+
+        indexer = other.get_indexer(self)
+        indexer = indexer.take((indexer != -1).nonzero()[0])
+        indexer = unique1d(indexer)
+
+        taken = other.take(indexer).values
+        return self._shallow_copy(taken)
 
     def _maybe_promote(self, other):
         if other.inferred_type == 'timedelta':
diff --git a/pandas/tests/indexes/timedeltas/test_setops.py b/pandas/tests/indexes/timedeltas/test_setops.py
index f7c3f764df0a0..afe0a19f509dc 100644
--- a/pandas/tests/indexes/timedeltas/test_setops.py
+++ b/pandas/tests/indexes/timedeltas/test_setops.py
@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 
 import pandas as pd
 from pandas import Int64Index, TimedeltaIndex, timedelta_range
@@ -73,3 +74,37 @@ def test_intersection_bug_1708(self):
         result = index_1 & index_2
         expected = timedelta_range('1 day 01:00:00', periods=3, freq='h')
         tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize('left, right, expected', [
+        (pd.to_timedelta(range(3), unit='s'),
+         pd.to_timedelta(range(2, -1, -1), unit='s'),
+         pd.to_timedelta(range(3), unit='s')),
+        (pd.to_timedelta(range(6, 3, -1), unit='s'),
+         pd.to_timedelta(range(5, 1, -1), unit='s'),
+         TimedeltaIndex(['00:00:05', '00:00:04'])),
+        (pd.to_timedelta(range(5, 1, -1), unit='s'),
+         pd.to_timedelta(range(6, 3, -1), unit='s'),
+         TimedeltaIndex(['00:00:05', '00:00:04'])),
+        (pd.to_timedelta(range(1, 20), unit='s'),
+         pd.to_timedelta((1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20), unit='s'),
+         pd.to_timedelta(range(1, 11), unit='s')),
+        (pd.to_timedelta((1, 2, 5, 6, 7), unit='s'),
+         pd.to_timedelta((3, 5, 6, 7), unit='s'),
+         pd.to_timedelta((5, 6, 7), unit='s')),
+        (pd.TimedeltaIndex(['00:00:09', '00:00:09', '00:00:07']),
+         pd.to_timedelta(range(10), unit='s'),
+         pd.TimedeltaIndex(['00:00:09', '00:00:07']))
+    ])
+    def test_intersect(self, left, right, expected):
+        # GH 17391
+        result = left.intersection(right)
+        tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize('idx', [
+        pd.to_timedelta(range(1, 2), unit='s'),
+        pd.to_timedelta(range(2, -1, -1), unit='s')
+    ])
+    def test_intersect_self(self, idx):
+        # GH 17391
+        result = idx.intersection(idx)
+        tm.assert_index_equal(idx, result)