diff --git a/CHANGES b/CHANGES
index 5ad1c3ece..d0f5c2875 100644
--- a/CHANGES
+++ b/CHANGES
@@ -13,6 +13,8 @@ Features added
 Bugs fixed
 ----------
 
+* #3597: python domain raises UnboundLocalError if invalid name given
+
 Testing
 --------
 
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index a6c223d89..11fa719dc 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -302,6 +302,7 @@ class PyObject(ObjectDescription):
         only the most recent object is tracked. This object prefix name will be
         removed with :py:meth:`after_content`.
         """
+        prefix = None
         if self.names:
             # fullname and name_prefix come from the `handle_signature` method.
             # fullname represents the full object name that is constructed using
@@ -312,8 +313,6 @@ class PyObject(ObjectDescription):
                 prefix = fullname
             elif name_prefix:
                 prefix = name_prefix.strip('.')
-            else:
-                prefix = None
         if prefix:
             self.env.ref_context['py:class'] = prefix
             if self.allow_nesting: