diff --git a/lib/templatesimplifier.cpp b/lib/templatesimplifier.cpp
index 1aad8738e..c721974f1 100644
--- a/lib/templatesimplifier.cpp
+++ b/lib/templatesimplifier.cpp
@@ -1249,12 +1249,15 @@ bool TemplateSimplifier::simplifyTemplateInstantiations(
                 ++indentlevel;
             else if (indentlevel > 0 && Token::Match(tok3, "> [,>]"))
                 --indentlevel;
-            templateMatchPattern += tok3->str();
-            templateMatchPattern += ' ';
+            bool constconst = tok3->str() == "const" && tok3->strAt(1) == "const";
+            if (!constconst) {
+                templateMatchPattern += tok3->str();
+                templateMatchPattern += ' ';
+            }
             if (indentlevel == 0 && Token::Match(tok3->previous(), "[<,]"))
                 typesUsedInTemplateInstantiation.push_back(tok3);
             // add additional type information
-            if (tok3->str() != "class") {
+            if (!constconst && tok3->str() != "class") {
                 if (tok3->isUnsigned())
                     typeForNewNameStr += "unsigned";
                 else if (tok3->isSigned())
diff --git a/test/testsimplifytemplate.cpp b/test/testsimplifytemplate.cpp
index 41c5a04af..6b553a167 100644
--- a/test/testsimplifytemplate.cpp
+++ b/test/testsimplifytemplate.cpp
@@ -85,6 +85,7 @@ private:
         TEST_CASE(template52);  // #6437 - crash upon valid code
         TEST_CASE(template53);  // #4335 - bail out for valid code
         TEST_CASE(template54);  // #6587 - memory corruption upon valid code
+        TEST_CASE(template55);  // #6604 - simplify "const const" to "const" in template instantiations
         TEST_CASE(template_unhandled);
         TEST_CASE(template_default_parameter);
         TEST_CASE(template_default_type);
@@ -961,6 +962,22 @@ private:
             "A<int> a;");
     }
 
+    void template55() { // #6604
+        ASSERT_EQUALS(
+            "class AtSmartPtr<T> : public ConstCastHelper < AtSmartPtr<constT> , T > { "
+            "friend struct ConstCastHelper < AtSmartPtr<constT> , T > ; "
+            "AtSmartPtr<T> ( const AtSmartPtr<T> & r ) ; "
+            "} ; "
+            "class AtSmartPtr<constT> : public ConstCastHelper < AtSmartPtr < const const T > , const T > { "
+            "friend struct ConstCastHelper < AtSmartPtr < const const T > , const T > ; "
+            "AtSmartPtr<constT> ( const AtSmartPtr<T> & r ) ; } ;",
+            tok("template<class T> class AtSmartPtr : public ConstCastHelper<AtSmartPtr<const T>, T>\n"
+                "{\n"
+                "    friend struct ConstCastHelper<AtSmartPtr<const T>, T>;\n"
+                "    AtSmartPtr(const AtSmartPtr<T>& r);\n"
+                "};"));
+    }
+
     void template_default_parameter() {
         {
             const char code[] = "template <class T, int n=3>\n"