diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index e1ac9e3309de7..2375617c19268 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -336,6 +336,7 @@ Timezones
 
 Numeric
 ^^^^^^^
+- Bug in :class:`RangeIndex` setting ``step`` incorrectly when being the subtrahend with minuend a numeric value (:issue:`53255`)
 - Bug in :meth:`Series.corr` and :meth:`Series.cov` raising ``AttributeError`` for masked dtypes (:issue:`51422`)
 - Bug in :meth:`Series.mean`, :meth:`DataFrame.mean` with object-dtype values containing strings that can be converted to numbers (e.g. "2") returning incorrect numeric results; these now raise ``TypeError`` (:issue:`36703`, :issue:`44008`)
 - Bug in :meth:`DataFrame.corrwith` raising ``NotImplementedError`` for pyarrow-backed dtypes (:issue:`52314`)
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index dd72ce30d290b..6837310ca8459 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -1015,8 +1015,9 @@ def _arith_method(self, other, op):
                 if not is_integer(rstep) or not rstep:
                     raise ValueError
 
+            # GH#53255
             else:
-                rstep = left.step
+                rstep = -left.step if op == ops.rsub else left.step
 
             with np.errstate(all="ignore"):
                 rstart = op(left.start, right)
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index 4edec0bf95982..b964fb43f1560 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -612,3 +612,9 @@ def test_sort_values_key(self):
 
     def test_cast_string(self, dtype):
         pytest.skip("casting of strings not relevant for RangeIndex")
+
+    def test_range_index_rsub_by_const(self):
+        # GH#53255
+        result = 3 - RangeIndex(0, 4, 1)
+        expected = RangeIndex(3, -1, -1)
+        tm.assert_index_equal(result, expected)