I have created a very simple html page. Below is the code of the html file
Client Login
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In short: NO you can not achieve what you'd like to do in the way you suggested. First off, you'd need to own said domain and have hosting for it.
That way you can now run your file (for this example we shall call it index.html)
Client Login
and now as you can see, your form action is set to Sign_up.php. You need this file to process your form, which I pressume you will write up. But here's a "placeholder" script in the mean time.
I just noticed you have a form to link to your sign-up page. Why not use an (ANCHOR) element which was designed for this kind of thing.
Sign Up Now