diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 0e6fb77e8b51b..ead1a2a4a544b 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -604,11 +604,6 @@ def _min_fitting_element(self, lower_limit: int) -> int:
         no_steps = -(-(lower_limit - self.start) // abs(self.step))
         return self.start + abs(self.step) * no_steps
 
-    def _max_fitting_element(self, upper_limit: int) -> int:
-        """Returns the largest element smaller than or equal to the limit"""
-        no_steps = (upper_limit - self.start) // abs(self.step)
-        return self.start + abs(self.step) * no_steps
-
     def _extended_gcd(self, a: int, b: int) -> tuple[int, int, int]:
         """
         Extended Euclidean algorithms to solve Bezout's identity:
diff --git a/pandas/tests/indexes/ranges/test_range.py b/pandas/tests/indexes/ranges/test_range.py
index e80868fb08a09..1b98f3c8194b5 100644
--- a/pandas/tests/indexes/ranges/test_range.py
+++ b/pandas/tests/indexes/ranges/test_range.py
@@ -369,24 +369,6 @@ def test_min_fitting_element(self):
         result = RangeIndex(5, big_num * 2, 1)._min_fitting_element(big_num)
         assert big_num == result
 
-    def test_max_fitting_element(self):
-        result = RangeIndex(0, 20, 2)._max_fitting_element(17)
-        assert 16 == result
-
-        result = RangeIndex(1, 6)._max_fitting_element(4)
-        assert 4 == result
-
-        result = RangeIndex(18, -2, -2)._max_fitting_element(17)
-        assert 16 == result
-
-        result = RangeIndex(5, 0, -1)._max_fitting_element(4)
-        assert 4 == result
-
-        big_num = 500000000000000000000000
-
-        result = RangeIndex(5, big_num * 2, 1)._max_fitting_element(big_num)
-        assert big_num == result
-
     def test_pickle_compat_construction(self):
         # RangeIndex() is a valid constructor
         pass