diff --git a/docs/changes.rst b/docs/changes.rst
index 4db24835..f42e7b85 100644
--- a/docs/changes.rst
+++ b/docs/changes.rst
@@ -11,6 +11,8 @@ skops Changelog
 
 v0.17
 -----
+- Fix ``skops update`` failing when a relative output path contains a
+  directory, including updates with ``--inplace``.
 - Loading a skops file now checks that each part of the file holds the kind
   of content its loader expects, for instance that the keyword arguments of a
   ``functools.partial`` are stored as a dict. A file that does not is refused
diff --git a/skops/cli/_update.py b/skops/cli/_update.py
index 8f07b1b9..8a801252 100644
--- a/skops/cli/_update.py
+++ b/skops/cli/_update.py
@@ -99,7 +99,9 @@ def _update_file(
         return None
 
     with tempfile.TemporaryDirectory() as tmp_dir:
-        tmp_output_file = Path(tmp_dir) / f"{output_file}.tmp"
+        # Only the file name is used, so a relative output path with directories
+        # (e.g. ``models/model.skops``) doesn't point into a missing directory.
+        tmp_output_file = Path(tmp_dir) / f"{Path(output_file).name}.tmp"
         dump(input_model, tmp_output_file)
         shutil.move(str(tmp_output_file), str(output_file))
     logger.info(f"Updated skops file written to {output_file}")
diff --git a/skops/cli/tests/test_update.py b/skops/cli/tests/test_update.py
index 1f28af39..0768dfbb 100644
--- a/skops/cli/tests/test_update.py
+++ b/skops/cli/tests/test_update.py
@@ -85,6 +85,23 @@ def test_base_case_works_as_expected(
         mock_logger.error.assert_not_called()
         mock_logger.debug.assert_not_called()
 
+    @pytest.mark.parametrize("inplace", [True, False])
+    def test_relative_path_with_directory(
+        self, tmp_path, monkeypatch, inplace: bool, dump_old_file, safe_obj
+    ):
+        # A relative output path with a directory component used to fail, since
+        # it was joined to the temporary directory as is.
+        monkeypatch.chdir(tmp_path.parent)
+        input_file = pathlib.Path(tmp_path.name) / f"{self.model_name}.skops"
+        output_file = None if inplace else input_file.with_name("updated.skops")
+
+        _update._update_file(
+            input_file=input_file, output_file=output_file, inplace=inplace
+        )
+
+        updated_obj = load(output_file or input_file)
+        assert np.array_equal(updated_obj, safe_obj)
+
     @mock.patch("skops.cli._update.dump")
     def test_only_diff(
         self, mock_dump: mock.MagicMock, skops_path: pathlib.Path, dump_old_file