Maintaining order in HashMap

I have a list which I convert to a map to do some work. After that, i convert the map back again to a list, but this time the order is random. I need the same initial order retained in my second list.

the obvious reason is that a HashMap doesn't maintain order. But I need to do something so that it does. I cannot change the Map implementation.How can I do that ?

Consider the given code:

import java.util.*;
public class Dummy {

public static void main(String[] args) {
    System.out.println("Hello world !");
    List<String> list = new ArrayList<String>();
    list.add("A");list.add("B");list.add("C");
    list.add("D");list.add("E");list.add("F");

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

    for(int i=0;i<list.size();i=i+2)
        map.put(list.get(i),list.get(i+1));

    // Use map here to do some work

    List<String> l= new ArrayList<String>();
    for (Map.Entry e : map.entrySet()) {
        l.add((String) e.getKey());
        l.add((String) e.getValue());
    }
  }
}

For ex - Initially, when I printed the list elements, it printed out

A B C D E F 

Now, when I print the elements of List l, it printed out

E F A B C D