更新表单字段而不刷新(防止重复的表单)

I need to update (submit) form without refresh. I know it should be done using Ajax, so I found many examples on this website, but none of them was useful in my case. Here's the catch - I don't need to display any "success" or similar messages when form was submitted, I need to display exactly the same form, but with new values.

Examining examples on this site, I got it working, but when form is submitted via ajax (this part works fine), I see two forms displayed. Here's the example - http://www.lipskas.com/form/ (the whole source is available to view)

What should I change here?

P.S. If I change "$('#msg').html(html);" to "$('#myForm').html(html);" duplicated form doesn't appear, except one "little" problem - the form can be submitted only for the 1st time. Then no more values are properly submitted.

In case you are interested why I need to display exactly the same form (but with updated fields) again, it's because I built some type of calculator which has many fields, and when user updates ANY field, re-calculations are made ( http://lipskas.com/bandymas/ )

Get rid of the "onclick" in the submit button and add this in the header above the chk function

<body>
<form id="myForm">
    <input type="text" name="username" value="submitted - "><br/>
    <input type="text" name="password" value="submitted - "><br/>
    <select name="some_array[1]"><option value="1">1</option><option value="2">2</option></select>
    <select name="some_stuff[2]"><option value="3">3</option><option value="4">4</option></select>
    <input type="submit" name="submit_ok" value="test me">
</form>
</body>

function chk(this)
{
$.ajax({
    type:"post",
    url:"index.php",
    data: this.serialize(),
    cache:false,
    success: function (html){
        $('body').html(html);
        }
});
}
$(function(){
$("body").on("submit","#myForm",function(){
chk($(this));
return false;
 });
 });