diff --git a/lib/checkclass.cpp b/lib/checkclass.cpp
index 7f90adee1..3022dce7c 100644
--- a/lib/checkclass.cpp
+++ b/lib/checkclass.cpp
@@ -2098,6 +2098,8 @@ void CheckClass::checkConst()
 
 bool CheckClass::isMemberVar(const SpaceInfo *info, const Token *tok)
 {
+    const Token *tok1 = tok;
+
     while (tok->previous() && !Token::Match(tok->previous(), "}|{|;|public:|protected:|private:|return|:|?"))
     {
         if (Token::Match(tok->previous(),  "* this"))
@@ -2109,7 +2111,7 @@ bool CheckClass::isMemberVar(const SpaceInfo *info, const Token *tok)
     if (tok->str() == "this")
         return true;
 
-    if (Token::Match(tok, "( * %var% ) ["))
+    if (Token::Match(tok, "( * %var% ) [") || (Token::Match(tok, "( * %var% ) <<") && tok1->next()->str() == "<<"))
         tok = tok->tokAt(2);
 
     // ignore class namespace
diff --git a/test/testclass.cpp b/test/testclass.cpp
index 31e222551..8a9a10cba 100644
--- a/test/testclass.cpp
+++ b/test/testclass.cpp
@@ -146,6 +146,7 @@ private:
         TEST_CASE(const35); // ticket #2001
         TEST_CASE(const36); // ticket #2003
         TEST_CASE(const37); // ticket #2081 and #2085
+        TEST_CASE(const38); // ticket #2135
         TEST_CASE(constoperator1);  // operator< can often be const
         TEST_CASE(constoperator2);	// operator<<
         TEST_CASE(constoperator3);
@@ -4088,6 +4089,23 @@ private:
         ASSERT_EQUALS("[test.cpp:9]: (style) The function 'Fred::isValid' can be const\n", errout.str());
     }
 
+    void const38() // ticket #2135
+    {
+        checkConst("class Foo {\n"
+                   "public:\n"
+                   "    ~Foo() { delete oArq; }\n"
+                   "    Foo(): oArq(new std::ofstream(\"...\")) {}\n"
+                   "    void MyMethod();\n"
+                   "private:\n"
+                   "    std::ofstream *oArq;\n"
+                   "};\n"
+                   "void Foo::MyMethod()\n"
+                   "{\n"
+                   "    (*oArq) << \"</table>\";\n"
+                   "}\n");
+        ASSERT_EQUALS("", errout.str());
+    }
+
     // increment/decrement => not const
     void constincdec()
     {