To get your latest facebook profile image you have to make sure you have a facebook username.

If you don’t have it visit Facebook Username to get a facebook username.

When you get your facebook username, URL of your facebook profile will look similar to

https://www.facebook.com/your_username/

To get your latest facebook profile image you have to use following url

http://graph.facebook.com/your_username/picture

Just replace your_username with your username

You can get your profile image by size. Following types are allowed to retrieve your profile image.
http://graph.facebook.com/your_username/picture?type=large

  1. type=small
  2. type=normal
  3. type=large
  4. type=square

Just replace type with actual value in following URL

http://graph.facebook.com/your_username/picture?type=large