diff --git a/Stream_support/include/CGAL/IO/STL.h b/Stream_support/include/CGAL/IO/STL.h
index 530dd5035f9..3854efa1f1d 100644
--- a/Stream_support/include/CGAL/IO/STL.h
+++ b/Stream_support/include/CGAL/IO/STL.h
@@ -84,7 +84,6 @@ bool read_STL(std::istream& is,
               )
 {
   const bool verbose = parameters::choose_parameter(parameters::get_parameter(np, internal_np::verbose), false);
-  const bool binary = CGAL::parameters::choose_parameter(CGAL::parameters::get_parameter(np, internal_np::use_binary_mode), true);
 
   if(!is.good())
   {
@@ -93,7 +92,6 @@ bool read_STL(std::istream& is,
     return false;
   }
 
-  int pos = 0;
   // Ignore all initial whitespace
   unsigned char c;
 
@@ -104,23 +102,11 @@ bool read_STL(std::istream& is,
       is.unget(); // move back to the first interesting char
       break;
     }
-    ++pos;
   }
 
   if(!is.good()) // reached the end
     return true;
 
-  // If we have gone beyond 80 characters and have not read anything yet,
-  // then this must be an ASCII file.
-  if(pos > 80)
-  {
-    if(binary)
-      return false;
-    return internal::parse_ASCII_STL(is, points, facets, verbose);
-  }
-
-  // We are within the first 80 characters, both ASCII and binary are possible
-
   // Read the 5 first characters to check if the first word is "solid"
   std::string s;
 
@@ -133,7 +119,6 @@ bool read_STL(std::istream& is,
      is.read(reinterpret_cast<char*>(&word[5]), sizeof(c)))
   {
     s = std::string(word, 5);
-    pos += 5;
   }
   else
   {
diff --git a/Stream_support/test/Stream_support/data/binary-issue-6374.stl b/Stream_support/test/Stream_support/data/binary-issue-6374.stl
new file mode 100644
index 00000000000..82709ac4a42
Binary files /dev/null and b/Stream_support/test/Stream_support/data/binary-issue-6374.stl differ
diff --git a/Stream_support/test/Stream_support/test_STL.cpp b/Stream_support/test/Stream_support/test_STL.cpp
index 9fd3dffe5f0..705ea72f7e5 100644
--- a/Stream_support/test/Stream_support/test_STL.cpp
+++ b/Stream_support/test/Stream_support/test_STL.cpp
@@ -79,8 +79,8 @@ int main(int argc, char** argv)
   assert(ok);
   std::cout << points.size() << " points and " << polygons.size() << " polygons" << std::endl;
 
-  if(argc == 0)
-    assert(points.size() == 434 && polygons.size() == 864);
+  if(argc == 1)
+    assert(points.size() == 4 && polygons.size() == 4);
 
   points.clear();
   polygons.clear();
@@ -129,6 +129,16 @@ int main(int argc, char** argv)
 
   further_tests();
 
+  // issue 6374
+  if(argc == 1)
+  {
+    points.clear();
+    polygons.clear();
+    bool ok = CGAL::IO::read_STL("data/binary-issue-6374.stl", points, polygons, CGAL::parameters::verbose(true));
+    assert(ok);
+    assert(points.size()==8 && polygons.size()==12);
+  }
+
   std::cout << "Done!" << std::endl;
   return EXIT_SUCCESS;
 }