diff --git a/lib/checkuninitvar.cpp b/lib/checkuninitvar.cpp
index 3b2e32ada..f717b04a2 100644
--- a/lib/checkuninitvar.cpp
+++ b/lib/checkuninitvar.cpp
@@ -1072,6 +1072,10 @@ void CheckUninitVar::checkScope(const Scope* scope)
             checkRhs(i->nameToken(), *i, NO_ALLOC, "");
             continue;
         }
+        if (Token::Match(i->nameToken(), "%var% ) (") && Token::simpleMatch(i->nameToken()->linkAt(2), ") =")) { // Function pointer is initialized, but Rhs might be not
+            checkRhs(i->nameToken()->linkAt(2)->next(), *i, NO_ALLOC, "");
+            continue;
+        }
 
         bool stdtype = _tokenizer->isC();
         const Token* tok = i->typeStartToken();
diff --git a/test/testuninitvar.cpp b/test/testuninitvar.cpp
index b617565c6..eee29398f 100644
--- a/test/testuninitvar.cpp
+++ b/test/testuninitvar.cpp
@@ -71,6 +71,7 @@ private:
         TEST_CASE(uninitvar8); // ticket #6230
         TEST_CASE(uninitvar9); // ticket #6424
         TEST_CASE(uninitvar_unconditionalTry);
+        TEST_CASE(uninitvar_funcptr); // #6404
 
         TEST_CASE(syntax_error); // Ticket #5073
 
@@ -2825,6 +2826,28 @@ private:
         ASSERT_EQUALS("[test.cpp:4]: (error) Uninitialized variable: i\n", errout.str());
     }
 
+    void uninitvar_funcptr() {
+        checkUninitVar2("void getLibraryContainer() {\n"
+                        "    Reference< XStorageBasedLibraryContainer >(*Factory)(const Reference< XComponentContext >&, const Reference< XStorageBasedDocument >&)\n"
+                        "        = &DocumentDialogLibraryContainer::create;\n"
+                        "    rxContainer.set((*Factory)(m_aContext, xDocument));\n"
+                        "}");
+        ASSERT_EQUALS("", errout.str());
+
+        checkUninitVar2("void getLibraryContainer() {\n"
+                        "    void* x;\n"
+                        "    Reference< XStorageBasedLibraryContainer >(*Factory)(const Reference< XComponentContext >&, const Reference< XStorageBasedDocument >&)\n"
+                        "        = x;\n"
+                        "    rxContainer.set((*Factory)(m_aContext, xDocument));\n"
+                        "}", "test.cpp", false);
+        ASSERT_EQUALS("[test.cpp:5]: (error) Uninitialized variable: x\n", errout.str());
+
+        checkUninitVar2("void getLibraryContainer() {\n"
+                        "    Reference< XStorageBasedLibraryContainer >(*Factory)(const Reference< XComponentContext >&, const Reference< XStorageBasedDocument >&);\n"
+                        "    rxContainer.set((*Factory)(m_aContext, xDocument));\n"
+                        "}");
+        ASSERT_EQUALS("[test.cpp:3]: (error) Uninitialized variable: Factory\n", errout.str());
+    }
     // Handling of function calls
     void uninitvar2_func() {
         // non-pointer variable