diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index fd1d3690e8a89..5edb031c7442c 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2316,16 +2316,38 @@ def shift(self, periods=1, freq=None):
 
     def argsort(self, *args, **kwargs):
         """
-        Returns the indices that would sort the index and its
-        underlying data.
+        Return the integer indicies that would sort the index.
+
+        Parameters
+        ----------
+        *args
+            Passed to `numpy.ndarray.argsort`.
+        **kwargs
+            Passed to `numpy.ndarray.argsort`.
 
         Returns
         -------
-        argsorted : numpy array
+        numpy.ndarray
+            Integer indicies that would sort the index if used as
+            an indexer.
 
         See also
         --------
-        numpy.ndarray.argsort
+        numpy.argsort : Similar method for NumPy arrays.
+        Index.sort_values : Return sorted copy of Index.
+
+        Examples
+        --------
+        >>> idx = pd.Index(['b', 'a', 'd', 'c'])
+        >>> idx
+        Index(['b', 'a', 'd', 'c'], dtype='object')
+
+        >>> order = idx.argsort()
+        >>> order
+        array([1, 0, 3, 2])
+
+        >>> idx[order]
+        Index(['a', 'b', 'c', 'd'], dtype='object')
         """
         result = self.asi8
         if result is None: