$(document).ready(function(){

    $("#registerForm").validate({

    rules: {

    Username: {required: true, minlength: 6},
    Password: {required: true, minlength: 6},
    re_Password: {required: true, equalTo: "#Password"}

    },

    });
});

<form id="registerForm" action="register.php" method="post" onsubmit="xmlhttpPost('register.php', 'registerForm', 'signup-box'); return false;">

<form method="post" id="registerForm" action="register.php">

$("#registerForm").submit(function(){

    if($("#registerForm").valid()){

        xmlhttpPost('register.php', 'registerForm', 'signup-box');

   }

return false;

});

$("form").submit(function(){
   if($("form").validate()){
      xmlhttpPost('register.php', 'registerForm', 'signup-box');
   }
   return false;
});

var $form = $("form");
    $form.validate({
        rules: {
            Username: {required: true, minlength: 6},
            Password: {required: true, minlength: 6},
            re_Password: {required: true, equalTo: "#Password"}
        },
        invalidHandler: function(event, validator) {
            // 'this' refers to the form
            var errors = validator.numberOfInvalids();
            if (errors) {
                var message = errors === 1
                  ? 'You missed 1 field. It has been highlighted'
                  : 'You missed ' + errors + ' fields. They have been highlighted';
            }
        },
        submitHandler: function (form) {

            var $form = $(form);
            $.ajax({
                url: destinationUrl,
                method: "POST",
                data: $form.serialize()
                })
                .done(function (result) {
                    // show some message, etc...

                    return false; // blocks redirect after submission via ajax
                })
                .fail(function (response, error) {
                    // failed
                })
                .always(function() {

                });
        }
    });