diff --git a/src/datasets/utils/py_utils.py b/src/datasets/utils/py_utils.py
index e233cd389e5..dbe17d45ed2 100644
--- a/src/datasets/utils/py_utils.py
+++ b/src/datasets/utils/py_utils.py
@@ -405,12 +405,18 @@ def _save_code(pickler, obj):
     # ex: <ipython-input-13-9ed2afe61d25> for ipython, and <stdin> for shell
     # Moreover lambda functions have a special name: '<lambda>'
     # ex: (lambda x: x).__code__.co_name == "<lambda>"  # True
+    #
     # For the hashing mechanism we ignore where the function has been defined
     # More specifically:
     # - we ignore the filename of special functions (filename starts with '<')
     # - we always ignore the line number
+    # - we only use the base name of the file instead of the whole path,
+    # to be robust in case a script is moved for example.
+    #
     # Only those two lines are different from the original implementation:
-    co_filename = "" if obj.co_filename.startswith("<") or obj.co_name == "<lambda>" else obj.co_filename
+    co_filename = (
+        "" if obj.co_filename.startswith("<") or obj.co_name == "<lambda>" else os.path.basename(obj.co_filename)
+    )
     co_firstlineno = 1
     # The rest is the same as in the original dill implementation
     if dill._dill.PY3:
diff --git a/tests/test_caching.py b/tests/test_caching.py
index 2cb39c23c10..6442f310b97 100644
--- a/tests/test_caching.py
+++ b/tests/test_caching.py
@@ -1,5 +1,8 @@
 import pickle
+import subprocess
 from hashlib import md5
+from pathlib import Path
+from textwrap import dedent
 from types import CodeType, FunctionType
 from unittest import TestCase
 from unittest.mock import patch
@@ -258,3 +261,28 @@ def test_hash_update(self):
     def test_hash_unpicklable(self):
         with self.assertRaises(pickle.PicklingError):
             Hasher.hash(UnpicklableCallable(Foo("hello")))
+
+
+def test_move_script_doesnt_change_hash(tmp_path: Path):
+    dir1 = tmp_path / "dir1"
+    dir2 = tmp_path / "dir2"
+    dir1.mkdir()
+    dir2.mkdir()
+    script_filename = "script.py"
+    code = dedent(
+        """
+    from datasets.fingerprint import Hasher
+    def foo():
+        pass
+    print(Hasher.hash(foo))
+    """
+    )
+    script_path1 = dir1 / script_filename
+    script_path2 = dir2 / script_filename
+    with script_path1.open("w") as f:
+        f.write(code)
+    with script_path2.open("w") as f:
+        f.write(code)
+    fingerprint1 = subprocess.check_output(["python", str(script_path1)])
+    fingerprint2 = subprocess.check_output(["python", str(script_path2)])
+    assert fingerprint1 == fingerprint2