diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index 1ec62857d..658d37499 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -9578,7 +9578,7 @@ void Tokenizer::simplifyOperatorName()
                     par = par->next();
                     done = false;
                 }
-                if (Token::Match(par, "[<>+-*&/=.!]") || Token::Match(par, "==|!=|<=|>="))
+                if (Token::Match(par, "[<>+-*&/=.!]") || Token::Match(par, "==|!=|<=|>=|>>|<<"))
                 {
                     op += par->str();
                     par = par->next();
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 07939f3dd..12ccf43ce 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -323,6 +323,7 @@ private:
         TEST_CASE(simplifyOperatorName2);
         TEST_CASE(simplifyOperatorName3);
         TEST_CASE(simplifyOperatorName4);
+        TEST_CASE(simplifyOperatorName5);
 
         // Some simple cleanups of unhandled macros in the global scope
         TEST_CASE(removeMacrosInGlobalScope);
@@ -5617,6 +5618,17 @@ private:
         ASSERT_EQUALS(result, tokenizeAndStringify(code,false));
     }
 
+    void simplifyOperatorName5()
+    {
+        const char code1[] = "std::istream & operator >> (std::istream & s, Fred &f);";
+        const char result1[] = "std :: istream & operator>> ( std :: istream & s , Fred & f ) ;";
+        ASSERT_EQUALS(result1, tokenizeAndStringify(code1,false));
+
+        const char code2[] = "std::ostream & operator << (std::ostream & s, const Fred &f);";
+        const char result2[] = "std :: ostream & operator<< ( std :: ostream & s , const Fred & f ) ;";
+        ASSERT_EQUALS(result2, tokenizeAndStringify(code2,false));
+    }
+
     void removeMacrosInGlobalScope()
     {
         // remove some unhandled macros in the global scope.