diff --git a/docs/whats-new.rst b/docs/whats-new.rst
index e91dae9e..a00ba543 100644
--- a/docs/whats-new.rst
+++ b/docs/whats-new.rst
@@ -4,7 +4,8 @@ What's new
 ==========
 0.6.1 (*unreleased*)
 --------------------
-
+- Properly rename the coordinate units (:pull:`351`).
+  By `Justus Magin <https://github.com/keewis>`_.
 
 0.6.0 (31 Aug 2025)
 -------------------
diff --git a/pint_xarray/index.py b/pint_xarray/index.py
index 7c233f3e..db031f83 100644
--- a/pint_xarray/index.py
+++ b/pint_xarray/index.py
@@ -112,7 +112,10 @@ def roll(self, shifts):
         return self._replace(self.index.roll(shifts))
 
     def rename(self, name_dict, dims_dict):
-        return self._replace(self.index.rename(name_dict, dims_dict))
+        new_units = {new: self.units[old] for old, new in name_dict.items()}
+        return self.__class__(
+            index=self.index.rename(name_dict, dims_dict), units=new_units
+        )
 
     def __getitem__(self, indexer):
         return self._replace(self.index[indexer])
diff --git a/pint_xarray/tests/test_index.py b/pint_xarray/tests/test_index.py
index 481fe7a5..1c9f6cf0 100644
--- a/pint_xarray/tests/test_index.py
+++ b/pint_xarray/tests/test_index.py
@@ -260,11 +260,12 @@ def test_roll(shifts, expected_index):
 @pytest.mark.parametrize("name_dict", ({"y2": "y3"}, {"y2": "y1"}))
 def test_rename(name_dict, dims_dict):
     wrapped_index = PandasIndex(pd.Index([1, 2], name="y2"), dim="y")
-    index = PintIndex(index=wrapped_index, units={"y": ureg.Unit("m")})
+    index = PintIndex(index=wrapped_index, units={"y2": ureg.Unit("m")})
 
     actual = index.rename(name_dict, dims_dict)
     expected = PintIndex(
-        index=wrapped_index.rename(name_dict, dims_dict), units=index.units
+        index=wrapped_index.rename(name_dict, dims_dict),
+        units={name_dict["y2"]: ureg.Unit("m")},
     )
 
     assert actual.equals(expected)