diff --git a/ci/code_checks.sh b/ci/code_checks.sh
index 9012dc6559a13..1b4121d14f1fc 100755
--- a/ci/code_checks.sh
+++ b/ci/code_checks.sh
@@ -70,7 +70,6 @@ if [[ -z "$CHECK" || "$CHECK" == "docstrings" ]]; then
         --format=actions \
         -i ES01 `# For now it is ok if docstrings are missing the extended summary` \
         -i "pandas.Series.dt PR01" `# Accessors are implemented as classes, but we do not document the Parameters section` \
-        -i "pandas.MultiIndex.reorder_levels RT03,SA01" \
         -i "pandas.NA SA01" \
         -i "pandas.NaT SA01" \
         -i "pandas.Period.freq GL08" \
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 500a5ad62fddc..878170c8377dc 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -2604,6 +2604,13 @@ def reorder_levels(self, order) -> MultiIndex:
         """
         Rearrange levels using input order. May not drop or duplicate levels.
 
+        `reorder_levels` is useful when you need to change the order of levels in
+        a MultiIndex, such as when reordering levels for hierarchical indexing. It
+        maintains the integrity of the MultiIndex, ensuring that all existing levels
+        are present and no levels are duplicated. This method is helpful for aligning
+        the index structure with other data structures or for optimizing the order
+        for specific data operations.
+
         Parameters
         ----------
         order : list of int or list of str
@@ -2613,6 +2620,13 @@ def reorder_levels(self, order) -> MultiIndex:
         Returns
         -------
         MultiIndex
+            A new MultiIndex with levels rearranged according to the specified order.
+
+        See Also
+        --------
+        MultiIndex.swaplevel : Swap two levels of the MultiIndex.
+        MultiIndex.set_names : Set names for the MultiIndex levels.
+        DataFrame.reorder_levels : Reorder levels in a DataFrame with a MultiIndex.
 
         Examples
         --------