Your form already has one button which is used to submit the data.

Reset

Copy the submit button line.  Paste it under itself.  Change submit to reset and change the value attribute from Send this info to Danger.  Save the page and load it in a browser.  Type something in the password field then press the reset (Danger) button.

If you use this make sure you consider what might happen if a user fills in a big form then accidentally presses the reset button rather than submit.

Button

If you just want a button which has no particular meaning then you can.  Submit buttons are assumed to send data in a form.  Reset clears the form.  The input type button can be used for anything you want but does nothing until you tell it to (probably using JavaScript). 

Create a new input element and:

To get it to do something you need JavaScript.  This is supposed to be about HTML but to test the button just add a new attribute to the button element:

onmouseup="document.getElementById('cookie').checked=false;"

When you press it this time watch the Keep me logged in checkbox.