diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 420788f9008cd..6cfc45e7690fa 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -714,7 +714,7 @@ def is_monotonic_decreasing(self):
         return if the index is monotonic decreasing (only equal or
         decreasing) values.
         """
-        return False
+        return not self.is_strictly_monotonic_increasing or self.nunique() == 1
 
     @cache_readonly
     def is_unique(self):