diff --git a/_unittests/ut_df/test_connex_split_cat.py b/_unittests/ut_df/test_connex_split_cat.py
index cf72d20..7aa8264 100644
--- a/_unittests/ut_df/test_connex_split_cat.py
+++ b/_unittests/ut_df/test_connex_split_cat.py
@@ -39,6 +39,37 @@ def test_cat_strat(self):
             lambda: train_test_apart_stratify(df, group="b", test_size=0.5), ValueError
         )
 
+    def test_cat_strat_sorted(self):
+        df = pandas.DataFrame(
+            [
+                dict(a=1, b="e"),
+                dict(a=2, b="e"),
+                dict(a=4, b="f"),
+                dict(a=8, b="f"),
+                dict(a=32, b="f"),
+                dict(a=16, b="f"),
+            ]
+        )
+
+        train, test = train_test_apart_stratify(
+            df, group="a", stratify="b", test_size=0.5, sorted_indices=True
+        )
+        self.assertEqual(train.shape[1], test.shape[1])
+        self.assertEqual(train.shape[0] + test.shape[0], df.shape[0])
+        c1 = Counter(train["b"])
+        c2 = Counter(train["b"])
+        self.assertEqual(c1, c2)
+
+        self.assertRaise(
+            lambda: train_test_apart_stratify(
+                df, group=None, stratify="b", test_size=0.5, sorted_indices=True
+            ),
+            ValueError,
+        )
+        self.assertRaise(
+            lambda: train_test_apart_stratify(df, group="b", test_size=0.5), ValueError
+        )
+
     def test_cat_strat_multi(self):
         df = pandas.DataFrame(
             [
diff --git a/pandas_streaming/df/connex_split.py b/pandas_streaming/df/connex_split.py
index ce9a3a2..21b82b0 100644
--- a/pandas_streaming/df/connex_split.py
+++ b/pandas_streaming/df/connex_split.py
@@ -1,5 +1,6 @@
 from collections import Counter
 from logging import getLogger
+from typing import Optional, Tuple
 import pandas
 import numpy
 from .dataframe_helpers import dataframe_shuffle
@@ -449,14 +450,15 @@ def double_merge(d):
 
 
 def train_test_apart_stratify(
-    df,
+    df: pandas.DataFrame,
     group,
-    test_size=0.25,
-    train_size=None,
-    stratify=None,
-    force=False,
-    random_state=None,
-):
+    test_size: Optional[float] = 0.25,
+    train_size: Optional[float] = None,
+    stratify: Optional[str] = None,
+    force: bool = False,
+    random_state: Optional[int] = None,
+    sorted_indices: bool = False,
+) -> Tuple["StreamingDataFrame", "StreamingDataFrame"]:  # noqa: F821
     """
     This split is for a specific case where data is linked
     in one way. Let's assume we have two ids as we have
@@ -474,6 +476,8 @@ def train_test_apart_stratify(
     :param force: if True, tries to get at least one example on the test side
         for each value of the column *stratify*
     :param random_state: seed for random generators
+    :param sorted_indices: sort index first,
+        see issue `41 <https://github.com/sdpython/pandas-streaming/issues/41>`
     :return: Two see :class:`StreamingDataFrame
         <pandas_streaming.df.dataframe.StreamingDataFrame>`, one
         for train, one for test.
@@ -540,10 +544,15 @@ def train_test_apart_stratify(
 
     split = {}
     for _, k in sorted_hist:
-        not_assigned = [c for c in ids[k] if c not in split]
+        indices = sorted(ids[k]) if sorted_indices else ids[k]
+        not_assigned, assigned = [], []
+        for c in indices:
+            if c in split:
+                assigned.append(c)
+            else:
+                not_assigned.append(c)
         if len(not_assigned) == 0:
             continue
-        assigned = [c for c in ids[k] if c in split]
         nb_test = sum(split[c] for c in assigned)
         expected = min(len(ids[k]), int(test_size * len(ids[k]) + 0.5)) - nb_test
         if force and expected == 0 and nb_test == 0: