diff --git a/clang/lib/Format/TokenAnnotator.cpp b/clang/lib/Format/TokenAnnotator.cpp
--- a/clang/lib/Format/TokenAnnotator.cpp
+++ b/clang/lib/Format/TokenAnnotator.cpp
@@ -116,10 +116,17 @@
     while (CurrentToken) {
       if (CurrentToken->is(tok::greater)) {
         // Try to do a better job at looking for ">>" within the condition of
-        // a statement.
+        // a statement. Conservatively insert spaces between consecutive ">"
+        // tokens to prevent splitting right bitshift operators and potentially
+        // altering program semantics. This check is overly conservative and
+        // will prevent spaces from being inserted in select nested template
+        // parameter cases, but should not alter program semantics.
         if (CurrentToken->Next && CurrentToken->Next->is(tok::greater) &&
             Left->ParentBracket != tok::less &&
-            isKeywordWithCondition(*Line.First))
+            (isKeywordWithCondition(*Line.First) ||
+             CurrentToken->getStartOfNonWhitespace() ==
+                 CurrentToken->Next->getStartOfNonWhitespace().getLocWithOffset(
+                     -1)))
           return false;
         Left->MatchingParen = CurrentToken;
         CurrentToken->MatchingParen = Left;
diff --git a/clang/unittests/Format/FormatTest.cpp b/clang/unittests/Format/FormatTest.cpp
--- a/clang/unittests/Format/FormatTest.cpp
+++ b/clang/unittests/Format/FormatTest.cpp
@@ -7649,6 +7649,8 @@
   verifyFormat("a<int> = 1;", Style);
   verifyFormat("a<int> >>= 1;", Style);
 
+  verifyFormat("test < a | b >> c;");
+  verifyFormat("test<test<a | b>> c;");
   verifyFormat("test >> a >> b;");
   verifyFormat("test << a >> b;");