Iterating through a LinkedHashMap in reverse order

I have a LinkedHashMap:

LinkedHashMap<String, RecordItemElement>

that I need to iterate through from a given key's position, backwards. So if I was given the 10th item's key, I'd need iterate backwards through the hashmap 9, 8, 7 etc.

The question requires a LinkedHashMap in reverse order, some answers suggesting using a TreeSet but this will reorder the map based upon the key.

This solution allows the iteration over the original LinkedHashMap not the new ArrayList as has also been proposed:

List<String> reverseOrderedKeys = new ArrayList<String>(linkedHashMap.keySet());
Collections.reverse(reverseOrderedKeys);
for (String key : reverseOrderedKeys) {
    RecordItemElement line = linkedHashMap.get(key);
}

The HashMap:

HashMap<Integer, String> map = new HashMap<Integer, String>();

Reverse iterating over values:

ListIterator<Sprite> iterator = new ArrayList<String>(map.values()).listIterator(map.size());
while (iterator.hasPrevious()) String value = iterator.previous();

Reverse iterating over keys:

ListIterator<Integer> iterator = new ArrayList(map.keySet()).listIterator(map.size());
while (iterator.hasPrevious()) Integer key = iterator.previous();

Reverse iterating over both:

ListIterator<Map.Entry<Integer, String>> iterator = new ArrayList<Map.Entry<Integer, String>>(map.entrySet()).listIterator(map.size());
while (iterator.hasPrevious()) Map.Entry<Integer, String> entry = iterator.previous();