diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index b28a53023ed..259e91083a7 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -7,6 +7,7 @@
 import numpy as np
 import pandas as pd
 import pytest
+from pandas.tseries.frequencies import to_offset
 
 import xarray as xr
 from xarray import (
@@ -2990,9 +2991,13 @@ def test_resample(self):
         actual = array.resample(time="24H").reduce(np.mean)
         assert_identical(expected, actual)
 
+        # Our use of `loffset` may change if we align our API with pandas' changes.
+        # ref https://github.com/pydata/xarray/pull/4537
         actual = array.resample(time="24H", loffset="-12H").mean()
-        expected = DataArray(array.to_series().resample("24H", loffset="-12H").mean())
-        assert_identical(expected, actual)
+        expected_ = array.to_series().resample("24H").mean()
+        expected_.index += to_offset("-12H")
+        expected = DataArray.from_series(expected_)
+        assert_identical(actual, expected)
 
         with raises_regex(ValueError, "index must be monotonic"):
             array[[2, 0, 1]].resample(time="1D")
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 2118bc8b780..916fb29f57f 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -9,6 +9,7 @@
 import pandas as pd
 import pytest
 from pandas.core.indexes.datetimes import DatetimeIndex
+from pandas.tseries.frequencies import to_offset
 
 import xarray as xr
 from xarray import (
@@ -3899,11 +3900,13 @@ def test_resample_loffset(self):
         )
         ds.attrs["dsmeta"] = "dsdata"
 
-        actual = ds.resample(time="24H", loffset="-12H").mean("time").time
-        expected = xr.DataArray(
-            ds.bar.to_series().resample("24H", loffset="-12H").mean()
-        ).time
-        assert_identical(expected, actual)
+        # Our use of `loffset` may change if we align our API with pandas' changes.
+        # ref https://github.com/pydata/xarray/pull/4537
+        actual = ds.resample(time="24H", loffset="-12H").mean().bar
+        expected_ = ds.bar.to_series().resample("24H").mean()
+        expected_.index += to_offset("-12H")
+        expected = DataArray.from_series(expected_)
+        assert_identical(actual, expected)
 
     def test_resample_by_mean_discarding_attrs(self):
         times = pd.date_range("2000-01-01", freq="6H", periods=10)