Index: clang/lib/Format/TokenAnnotator.cpp
===================================================================
--- clang/lib/Format/TokenAnnotator.cpp
+++ clang/lib/Format/TokenAnnotator.cpp
@@ -2281,6 +2281,10 @@
         Next = Next->Next;
         continue;
       }
+      if (Next->is(TT_TemplateOpener) && Next->MatchingParen) {
+        Next = Next->MatchingParen;
+        continue;
+      }
 
       break;
     }
@@ -2810,6 +2814,10 @@
                                     tok::l_square));
   if (Right.is(tok::star) && Left.is(tok::l_paren))
     return false;
+  if (Right.is(tok::star) && Left.is(tok::star))
+    return false;
+  if (Right.is(tok::star) && Left.is(TT_TemplateCloser))
+    return false;
   if (Right.isOneOf(tok::star, tok::amp, tok::ampamp)) {
     const FormatToken *Previous = &Left;
     while (Previous && !Previous->is(tok::kw_operator)) {
Index: clang/unittests/Format/FormatTest.cpp
===================================================================
--- clang/unittests/Format/FormatTest.cpp
+++ clang/unittests/Format/FormatTest.cpp
@@ -6279,7 +6279,15 @@
                "void\n"
                "A::operator[]() {}\n"
                "void\n"
-               "A::operator!() {}\n",
+               "A::operator!() {}\n"
+               "void\n"
+               "A::operator**() {}\n"
+               "void\n"
+               "A::operator<Foo>*() {}\n"
+               "void\n"
+               "A::operator<Foo>**() {}\n"
+               "void\n"
+               "A::operator void **() {}\n",
                Style);
   verifyFormat("constexpr auto\n"
                "operator()() const -> reference {}\n"
@@ -15628,9 +15636,15 @@
   Style.PointerAlignment = FormatStyle::PAS_Right;
   verifyFormat("Foo::operator*();", Style);
   verifyFormat("Foo::operator void *();", Style);
+  verifyFormat("Foo::operator void **();", Style);
   verifyFormat("Foo::operator()(void *);", Style);
   verifyFormat("Foo::operator*(void *);", Style);
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator**();", Style);
+  verifyFormat("Foo::operator<int>*();", Style);
+  verifyFormat("Foo::operator<Foo>*();", Style);
+  verifyFormat("Foo::operator<int>**();", Style);
+  verifyFormat("Foo::operator<Foo>**();", Style);
   verifyFormat("operator*(int (*)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&();", Style);
@@ -15650,12 +15664,17 @@
   Style.PointerAlignment = FormatStyle::PAS_Left;
   verifyFormat("Foo::operator*();", Style);
   verifyFormat("Foo::operator void*();", Style);
+  verifyFormat("Foo::operator void**();", Style);
   verifyFormat("Foo::operator/*comment*/ void*();", Style);
   verifyFormat("Foo::operator/*a*/ const /*b*/ void*();", Style);
   verifyFormat("Foo::operator/*a*/ volatile /*b*/ void*();", Style);
   verifyFormat("Foo::operator()(void*);", Style);
   verifyFormat("Foo::operator*(void*);", Style);
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator<int>*();", Style);
+  verifyFormat("Foo::operator<Foo>*();", Style);
+  verifyFormat("Foo::operator<int>**();", Style);
+  verifyFormat("Foo::operator<Foo>**();", Style);
   verifyFormat("operator*(int (*)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&();", Style);