Step 1: First you have to Open your Timeline and Open your Profile Picture Album by clicking on Photos Tab, Choose a Picture that you want as another Profile Picture.
Step 2: Open that Picture in a New Window By Holding Ctrl and Clicking on it.
Step 3: Now Check the URL of that Picture, you will get something like below URL.
https://www.facebook.com/photo.php?fbid=491366447588908&set=a.108695719189318.5863.100001466701828&type
All you have to do is Copy the fbid, Here in the above url, my photo fbid is 491366447588908.
Step 5: A popup window will appear, now Right Click on your Profile Picture and Choose Inspect Element.
Step 6: Now click on the Small arrow to Expand the Code Further.
Now all You need to do is Replace the Current fbid Value with the one you Copied earlier in Step 3, You can do it by Double Clicking on the Current fbid Value and Replace it with the one you Copied earlier which is in my case :491366447588908.
Step 7: Click anywhere , Close Inspect Element Window and Now Click on Save, All Done, Now Check your timeline, update any status and you will see Different Profile Picture.