diff --git a/lib/templatesimplifier.cpp b/lib/templatesimplifier.cpp
index ae17b1a0f..cf86990f0 100644
--- a/lib/templatesimplifier.cpp
+++ b/lib/templatesimplifier.cpp
@@ -225,6 +225,7 @@ unsigned int TemplateSimplifier::templateParameters(const Token *tok)
 
         if (!tok)
             return 0;
+
         // ,/>
         while (tok->str() == ">" || tok->str() == ">>") {
             if (level == 0)
@@ -236,9 +237,15 @@ unsigned int TemplateSimplifier::templateParameters(const Token *tok)
                 --level;
             }
             tok = tok->next();
+
+            // * / &
+            while (Token::Match(tok, "[*&]"))
+                tok = tok->next();
+
             if (!tok)
                 return 0;
         }
+
         if (tok->str() != ",")
             continue;
         if (level == 0)
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 4927a2494..796eb743b 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -259,6 +259,7 @@ private:
         TEST_CASE(varid_using);  // ticket #3648
         TEST_CASE(varid_catch);
         TEST_CASE(varid_functionPrototypeTemplate);
+        TEST_CASE(varid_templatePtr); // #4319
 
         TEST_CASE(varidclass1);
         TEST_CASE(varidclass2);
@@ -4057,6 +4058,11 @@ private:
                       "1: function < void ( ) > fptr@1 ;\n", tokenizeDebugListing("function<void(void)> fptr;"));
     }
 
+    void varid_templatePtr() {
+        ASSERT_EQUALS("\n\n##file 0\n"
+                      "1: std :: map < int , FooTemplate < int > * > dummy_member@1 [ 1 ] ;\n", tokenizeDebugListing("std::map<int, FooTemplate<int>*> dummy_member[1];"));
+    }
+
     void varidclass1() {
         const std::string actual = tokenizeDebugListing(
                                        "class Fred\n"