diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 95ea60d3..49aac90d 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -14,6 +14,11 @@ Added
 -----
 - Python 3.10 support.
 
+Fixed
+-----
+- The inverse indices returned from `Rotation.unique()` now correctly recreate the
+  original `Rotation` instance.
+
 2021-12-21 - version 0.8.0
 ==========================
 
diff --git a/orix/quaternion/rotation.py b/orix/quaternion/rotation.py
index c20cf574..fc35292c 100644
--- a/orix/quaternion/rotation.py
+++ b/orix/quaternion/rotation.py
@@ -158,7 +158,12 @@ def unique(self, return_index=False, return_inverse=False, antipodal=True):
                 axis=-1,
             ).round(6)
         _, idx, inv = np.unique(abcd, axis=0, return_index=True, return_inverse=True)
-        idx_sort = np.sort(idx)
+        idx_argsort = np.argsort(idx)
+        idx_sort = idx[idx_argsort]
+        # build inverse index map
+        inv_map = np.empty_like(idx_argsort)
+        inv_map[idx_argsort] = np.arange(idx_argsort.size)
+        inv = inv_map[inv]
         dat = rotation[idx_sort]
         dat.improper = rotation.improper[idx_sort]
         if return_index and return_inverse:
diff --git a/orix/tests/quaternion/test_rotation.py b/orix/tests/quaternion/test_rotation.py
index 4a27c1a2..e94d7a72 100644
--- a/orix/tests/quaternion/test_rotation.py
+++ b/orix/tests/quaternion/test_rotation.py
@@ -299,6 +299,13 @@ def test_kwargs_unique(rotation):
     rotation.unique(return_index=False, return_inverse=True)
 
 
+def test_unique_inverse():
+    r = Rotation.random((20,))
+    u, inverse = r.unique(return_inverse=True)
+    m = u[inverse] * ~r
+    assert np.allclose(m.angle.data, 0)
+
+
 @pytest.mark.parametrize(
     "rotation, improper, expected, improper_expected",
     [