diff --git a/Lib/test/test_xml_etree.py b/Lib/test/test_xml_etree.py
index 08f7988..22fafa9 100644
--- a/Lib/test/test_xml_etree.py
+++ b/Lib/test/test_xml_etree.py
@@ -1841,6 +1841,15 @@
 
     """
 
+def check_issue10777():
+    """
+    Registering a namespace twice caused a "dictionary changed size during
+    iteration" bug.
+
+    >>> ET.register_namespace('test10777', 'http://myuri/')
+    >>> ET.register_namespace('test10777', 'http://myuri/')
+    """
+
 # --------------------------------------------------------------------
 
 
diff --git a/Lib/xml/etree/ElementTree.py b/Lib/xml/etree/ElementTree.py
index 53aa9e7..ba33879 100644
--- a/Lib/xml/etree/ElementTree.py
+++ b/Lib/xml/etree/ElementTree.py
@@ -1068,7 +1068,7 @@
 def register_namespace(prefix, uri):
     if re.match("ns\d+$", prefix):
         raise ValueError("Prefix format reserved for internal use")
-    for k, v in _namespace_map.items():
+    for k, v in list(_namespace_map.items()):
         if k == uri or v == prefix:
             del _namespace_map[k]
     _namespace_map[uri] = prefix
diff --git a/Misc/NEWS b/Misc/NEWS
index 8acc9e3..46b6233 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -18,6 +18,9 @@
 Library
 -------
 
+- Issue #10777: Fix "dictionary changed size during iteration" bug in
+  ElementTree register_namespace().
+
 - Issue #10626: test_logging now preserves logger disabled states.
 
 - Issue #10774: test_logging now removes temp files created during tests.