diff --git a/clang/lib/Sema/SemaCodeComplete.cpp b/clang/lib/Sema/SemaCodeComplete.cpp
--- a/clang/lib/Sema/SemaCodeComplete.cpp
+++ b/clang/lib/Sema/SemaCodeComplete.cpp
@@ -9648,7 +9648,8 @@
           if (!(Filename.endswith_insensitive(".h") ||
                 Filename.endswith_insensitive(".hh") ||
                 Filename.endswith_insensitive(".hpp") ||
-                Filename.endswith_insensitive(".inc")))
+                Filename.endswith_insensitive(".inc") ||
+                !Filename.contains('.')))
             break;
         }
         AddCompletion(Filename, /*IsDirectory=*/false);
diff --git a/clang/test/CodeCompletion/included-files.cpp b/clang/test/CodeCompletion/included-files.cpp
--- a/clang/test/CodeCompletion/included-files.cpp
+++ b/clang/test/CodeCompletion/included-files.cpp
@@ -22,12 +22,12 @@
 // CHECK-3-NOT: foo.h>
 // CHECK-3: foosys>
 
-// With -I rather than -isystem, the header extension is required.
+// A header extension is not required.
 #include <foosys>
 // RUN: %clang -fsyntax-only -I %t/a -Xclang -code-completion-at=%t/main.cc:26:13 %t/main.cc | FileCheck -check-prefix=CHECK-4 %s
 // CHECK-4-NOT: foo.cc>
 // CHECK-4-NOT: foo.h>
-// CHECK-4-NOT: foosys>
+// CHECK-4: foosys>
 
 // Backslash handling.
 #include "a\foosys"