How to check/uncheck radio button on click?

I want to be able to uncheck a radio button by clicking on it.

So, if a radio button is unchecked, I want to check it, if it is checked, I want to uncheck it.

This does not work:

$('input[type=radio]:checked').click(function(){
    $(this).attr('checked', false);
});

I am not able to check a radio button now.