diff --git a/lib/checkclass.cpp b/lib/checkclass.cpp
index 4f4757fb4..3a6bc79d0 100644
--- a/lib/checkclass.cpp
+++ b/lib/checkclass.cpp
@@ -2108,12 +2108,12 @@ void CheckClass::checkConst()
             if (!scope->definedType->derivedFrom.empty() && func.isImplicitlyVirtual(true))
                 continue;
 
-            bool memberAccessed = false;
+            enum MemberAccess memberAccessed = MemberAccess::NONE;
             // if nothing non-const was found. write error..
             if (!checkConstFunc(scope, &func, memberAccessed))
                 continue;
 
-            const bool suggestStatic = !memberAccessed && !func.isOperator();
+            const bool suggestStatic = memberAccessed != MemberAccess::MEMBER && !func.isOperator();
             if ((returnsPtrOrRef || func.isConst()) && !suggestStatic)
                 continue;
 
@@ -2293,7 +2293,7 @@ bool CheckClass::isConstMemberFunc(const Scope *scope, const Token *tok)
 
 const std::set<std::string> CheckClass::stl_containers_not_const = { "map", "unordered_map", "std :: map|unordered_map <" }; // start pattern
 
-bool CheckClass::checkConstFunc(const Scope *scope, const Function *func, bool& memberAccessed) const
+bool CheckClass::checkConstFunc(const Scope *scope, const Function *func, MemberAccess& memberAccessed) const
 {
     if (mTokenizer->hasIfdef(func->functionScope->bodyStart, func->functionScope->bodyEnd))
         return false;
@@ -2312,9 +2312,10 @@ bool CheckClass::checkConstFunc(const Scope *scope, const Function *func, bool&
 
     auto checkFuncCall = [this, &memberAccessed](const Token* funcTok, const Scope* scope, const Function* func) {
         if (isMemberFunc(scope, funcTok) && (funcTok->strAt(-1) != "." || Token::simpleMatch(funcTok->tokAt(-2), "this ."))) {
-            if (!isConstMemberFunc(scope, funcTok) && func != funcTok->function())
+            const bool isSelf = func == funcTok->function();
+            if (!isConstMemberFunc(scope, funcTok) && !isSelf)
                 return false;
-            memberAccessed = true;
+            memberAccessed = (isSelf && memberAccessed != MemberAccess::MEMBER) ? MemberAccess::SELF : MemberAccess::MEMBER;
         }
 
         if (const Function* f = funcTok->function()) { // check known function
@@ -2361,7 +2362,7 @@ bool CheckClass::checkConstFunc(const Scope *scope, const Function *func, bool&
     // it can be a const function..
     for (const Token *tok1 = func->functionScope->bodyStart; tok1 && tok1 != func->functionScope->bodyEnd; tok1 = tok1->next()) {
         if (tok1->isName() && isMemberVar(scope, tok1)) {
-            memberAccessed = true;
+            memberAccessed = MemberAccess::MEMBER;
             const Variable* v = tok1->variable();
             if (v && v->isMutable())
                 continue;
@@ -2476,7 +2477,7 @@ bool CheckClass::checkConstFunc(const Scope *scope, const Function *func, bool&
                     ;
                 } else if (hasOverloadedMemberAccess(end, var->typeScope())) {
                     ;
-                } else if (!var->typeScope() || !isConstMemberFunc(var->typeScope(), end))
+                } else if (!var->typeScope() || (end->function() != func && !isConstMemberFunc(var->typeScope(), end)))
                     return false;
             }
 
diff --git a/lib/checkclass.h b/lib/checkclass.h
index 4a940857f..a2303774d 100644
--- a/lib/checkclass.h
+++ b/lib/checkclass.h
@@ -319,7 +319,8 @@ private:
     bool isMemberVar(const Scope *scope, const Token *tok) const;
     static bool isMemberFunc(const Scope *scope, const Token *tok);
     static bool isConstMemberFunc(const Scope *scope, const Token *tok);
-    bool checkConstFunc(const Scope *scope, const Function *func, bool& memberAccessed) const;
+    enum class MemberAccess { NONE, SELF, MEMBER };
+    bool checkConstFunc(const Scope *scope, const Function *func, MemberAccess& memberAccessed) const;
 
     // constructors helper function
     /** @brief Information about a member variable. Used when checking for uninitialized variables */
diff --git a/test/testclass.cpp b/test/testclass.cpp
index 7be1486d6..4119f8e2f 100644
--- a/test/testclass.cpp
+++ b/test/testclass.cpp
@@ -6539,8 +6539,8 @@ private:
                       errout.str());
     }
 
-    void const89() { // #11654
-        checkConst("struct S {\n"
+    void const89() {
+        checkConst("struct S {\n" // #11654
                    "    void f(bool b);\n"
                    "    int i;\n"
                    "};\n"
@@ -6560,6 +6560,23 @@ private:
                    "        f(i);\n"
                    "}\n");
         ASSERT_EQUALS("", errout.str());
+
+        checkConst("struct S {\n" // #11744
+                   "    S* p;\n"
+                   "    int f() {\n"
+                   "        if (p)\n"
+                   "            return 1 + p->f();\n"
+                   "        return 1;\n"
+                   "    }\n"
+                   "    int g(int i) {\n"
+                   "        if (i > 0)\n"
+                   "            return i + g(i - 1);\n"
+                   "        return 0;\n"
+                   "    }\n"
+                   "};\n");
+        ASSERT_EQUALS("[test.cpp:3]: (style, inconclusive) Technically the member function 'S::f' can be const.\n"
+                      "[test.cpp:8]: (performance, inconclusive) Technically the member function 'S::g' can be static (but you may consider moving to unnamed namespace).\n",
+                      errout.str());
     }
 
     void const90() { // #11637