diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 3f89b0619e600..d1d71e584ae3d 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2379,6 +2379,10 @@ def unique(self, level=None):
         """
         if level is not None:
             self._validate_index_level(level)
+
+        if self.is_unique:
+            return self._shallow_copy()
+
         result = super().unique()
         return self._shallow_copy(result)
 
@@ -2864,7 +2868,7 @@ def _intersection(self, other, sort=False):
             result = algos.safe_sort(result)
 
         # Intersection has to be unique
-        assert algos.unique(result).shape == result.shape
+        assert Index(result).is_unique
 
         return result