diff --git a/Changelog.rst b/Changelog.rst
index cfb32e6c..b195f0fc 100644
--- a/Changelog.rst
+++ b/Changelog.rst
@@ -3,6 +3,7 @@ Version ?.?.?
 
 **2026-??-??**
 
+* Add ``__orthogonal_indexing__`` flag by `David Hassell <https://github.com/davidhassell>`_ in https://github.com/NCAS-CMS/pyfive/issue/171
 * Allow negative slices when indexing chunked data by `David Hassell <https://github.com/davidhassell>`_ in https://github.com/NCAS-CMS/pyfive/pull/170
 
 Version 1.0.1
diff --git a/pyfive/high_level.py b/pyfive/high_level.py
index eddfac3b..1ab5e906 100644
--- a/pyfive/high_level.py
+++ b/pyfive/high_level.py
@@ -16,6 +16,7 @@
 from pyfive.dataobjects import DataObjects, DatasetID
 from pyfive.misc_low_level import SuperBlock
 from pyfive.h5py import Datatype
+from pyfive.p5t import P5VlenStringType, P5ReferenceType, P5SequenceType
 
 
 class Group(Mapping):
@@ -502,6 +503,37 @@ def attrs(self):
         """attrs attribute."""
         return self.id._meta.attributes
 
+    @property
+    def __orthogonal_indexing__(self):
+        """Flag to indicate whether indexing is orthogonal.
+
+        In general, the flag will be `True` if:
+
+        * The data is chunked.
+        * The data is contiguous and memory mapped access is not
+          available.
+
+        """
+        if self.id.chunks is not None:
+            # Chunked data indexed with
+            # `DatasetID._get_selection_via_chunks`
+            return True
+
+        if (
+            not (
+                isinstance(
+                    self.id._ptype, (P5ReferenceType, P5VlenStringType, P5SequenceType)
+                )
+            )
+            and not self.id.posix
+        ):
+            # Contiguous data indexed with
+            # `DatasetID._get_direct_from_contiguous`
+            return True
+
+        # All other cases
+        return False
+
 
 class DimensionManager(Sequence):
     """Represents a collection of dimensions associated with a dataset."""
diff --git a/tests/test_dataset_indexing.py b/tests/test_dataset_indexing.py
index 970e75ac..63e4c73a 100644
--- a/tests/test_dataset_indexing.py
+++ b/tests/test_dataset_indexing.py
@@ -10,6 +10,7 @@
 
 DIRNAME = os.path.dirname(__file__)
 DATASET_CHUNKED_FILE = os.path.join(DIRNAME, "data/chunked.hdf5")
+DATASET_CONTIGUOUS_FILE = os.path.join(DIRNAME, "data/dataset_multidim.hdf5")
 
 
 # Define a fixture that opens the chunked file once
@@ -19,6 +20,13 @@ def chunked_file():
         yield hfile
 
 
+# Define a fixture that opens the contiguous file once
+@pytest.fixture(scope="module")
+def contiguous_file():
+    with pyfive.File(DATASET_CONTIGUOUS_FILE) as hfile:
+        yield hfile
+
+
 @pytest.mark.parametrize(
     "index",
     [
@@ -65,3 +73,8 @@ def test_dataset_indexing_replace_negative_slices():
     # Can't pass in in Ellipsis
     with pytest.raises(ValueError) as error:
         func((0, slice(6, 0, -2), ...), (7, 8, 9))
+
+
+def test_dataset_orthogonal_indexing(chunked_file, contiguous_file):
+    assert chunked_file["dataset1"].__orthogonal_indexing__ is True
+    assert contiguous_file["d"].__orthogonal_indexing__ is False