diff --git a/lib/templatesimplifier.cpp b/lib/templatesimplifier.cpp
index 09d17c843..d2278daad 100644
--- a/lib/templatesimplifier.cpp
+++ b/lib/templatesimplifier.cpp
@@ -86,7 +86,7 @@ void TemplateSimplifier::cleanupAfterSimplify(Token *tokens)
                     end = end->link()->next();
                     break;
                 }
-                if (!Token::Match(end, "%name%|::|<|>|>>|,")) {
+                if (!Token::Match(end, "%name%|::|<|>|,")) {
                     end = nullptr;
                     break;
                 }
@@ -564,10 +564,10 @@ void TemplateSimplifier::useDefaultArgumentValues(const std::list<Token *> &temp
                 ++templateParmDepth;
 
             // end of template parameters?
-            if (Token::Match(tok, ">|>>")) {
-                if (Token::Match(tok, ">|>> class|struct %name%"))
+            if (tok->str() == ">") {
+                if (Token::Match(tok, "> class|struct %name%"))
                     classname = tok->strAt(2);
-                templateParmDepth -= (1 + (tok->str() == ">>"));
+                --templateParmDepth;
                 if (0 == templateParmDepth)
                     break;
             }
@@ -649,11 +649,7 @@ void TemplateSimplifier::useDefaultArgumentValues(const std::list<Token *> &temp
                     ++indentlevel;
                 } else if (indentlevel > 0 && tok2->str() == ">")
                     --indentlevel;
-                else if (indentlevel > 0 && tok2->str() == ">>") {
-                    indentlevel -= 2;
-                    if (indentlevel < 0)
-                        tok2->str(">");
-                } else if (indentlevel == 0 && Token::Match(tok2, ",|>|>>"))
+                else if (indentlevel == 0 && Token::Match(tok2, ",|>"))
                     break;
                 if (indentlevel < 0)
                     break;
@@ -680,13 +676,11 @@ bool TemplateSimplifier::instantiateMatch(const Token *instance, const std::stri
     if (patternAfter) {
         const Token *tok = instance;
         unsigned int indentlevel = 0;
-        for (tok = instance; tok && (tok->str() != ">" || indentlevel > 0) && (tok->str() != ">>" || indentlevel > 1); tok = tok->next()) {
+        for (tok = instance; tok && (tok->str() != ">" || indentlevel > 0); tok = tok->next()) {
             if (Token::Match(tok, "[<,] %name% <") && templateParameters(tok->tokAt(2)) > 0)
                 ++indentlevel;
             if (indentlevel > 0 && tok->str() == ">")
                 --indentlevel;
-            if (indentlevel > 0 && tok->str() == ">>")
-                indentlevel -= (indentlevel > 1) ? 2 : 1;
         }
         if (!tok || !Token::Match(tok->next(), patternAfter))
             return false;
@@ -779,17 +773,12 @@ void TemplateSimplifier::expandTemplate(
                 if (itype < typeParametersInDeclaration.size()) {
                     unsigned int typeindentlevel = 0;
                     for (const Token *typetok = typesUsedInTemplateInstantiation[itype];
-                         typetok && (typeindentlevel>0 || !Token::Match(typetok, ",|>|>>"));
+                         typetok && (typeindentlevel>0 || !Token::Match(typetok, ",|>"));
                          typetok = typetok->next()) {
                         if (Token::Match(typetok, "%name% <") && templateParameters(typetok->next()) > 0)
                             ++typeindentlevel;
                         else if (typeindentlevel > 0 && typetok->str() == ">")
                             --typeindentlevel;
-                        else if (typeindentlevel > 0 && typetok->str() == ">>") {
-                            if (typeindentlevel == 1)
-                                break;
-                            typeindentlevel -= 2;
-                        }
                         tokenlist.addtoken(typetok, tok3->linenr(), tok3->fileIndex());
                     }
                     continue;
@@ -1260,15 +1249,7 @@ bool TemplateSimplifier::simplifyTemplateInstantiations(
                 ++indentlevel;
             else if (indentlevel > 0 && Token::Match(tok3, "> [,>]"))
                 --indentlevel;
-            else if (indentlevel > 0 && tok3->str() == ">>") {
-                if (indentlevel == 1) {
-                    templateMatchPattern += '>';
-                    typeForNewNameStr += '>';
-                    break;
-                }
-                indentlevel -= 2;
-            }
-            templateMatchPattern += (tok3->str() == ">>") ? std::string("> >") : tok3->str();
+            templateMatchPattern += tok3->str();
             templateMatchPattern += ' ';
             if (indentlevel == 0 && Token::Match(tok3->previous(), "[<,]"))
                 typesUsedInTemplateInstantiation.push_back(tok3);
diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index 4bfb8f466..cd48b797b 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -2368,7 +2368,7 @@ static bool setVarIdParseDeclaration(const Token **tok, const std::map<std::stri
         } else if ((TemplateSimplifier::templateParameters(tok2) > 0) ||
                    Token::simpleMatch(tok2, "< >") /* Ticket #4764 */) {
             tok2 = tok2->findClosingBracket();
-            if (!Token::Match(tok2, ">|>>"))
+            if (tok2->str() != ">")
                 break;
             singleNameCount = 1;
         } else if (Token::Match(tok2, "&|&&")) {
@@ -2964,14 +2964,10 @@ void Tokenizer::createLinks2()
                 type.pop();
         else if (token->str() == "<" && token->previous() && token->previous()->isName() && !token->previous()->varId())
             type.push(token);
-        else if (Token::Match(token, ">|>>")) {
+        else if (token->str() == ">") {
             if (type.empty() || type.top()->str() != "<") // < and > don't match.
                 continue;
-            if (token->next() && !Token::Match(token->next(), "%name%|>|>>|&|*|::|,|(|)|{|;|["))
-                continue;
-
-            // Check type of open link
-            if (token->str() == ">>" && type.size() < 2)
+            if (token->next() && !Token::Match(token->next(), "%name%|>|&|*|::|,|(|)|{|;|["))
                 continue;
 
             // if > is followed by [ .. "new a<b>[" is expected
@@ -2987,15 +2983,6 @@ void Tokenizer::createLinks2()
 
             Token* top = type.top();
             type.pop();
-            if (token->str() == ">>" && type.top()->str() != "<") {
-                type.push(top);
-                continue;
-            }
-
-            if (token->str() == ">>") { // C++11 right angle bracket
-                token->str(">");
-                token->insertToken(">");
-            }
 
             Token::createMutualLinks(top, token);
         }