Edit in JSFiddle

$(".dropdown img.flag").addClass("flagvisibility");

$(".dropdown dt a").click(function() {
  $(".dropdown dd ul").toggle();
});

$(".dropdown dd ul li a").click(function() {
  var text = $(this).html();
  $(".dropdown dt a span").html(text);
  $(".dropdown dd ul").hide();
  /* $("#result").html("Selected value is: " + getSelectedValue("sample"));*/
});

function getSelectedValue(id) {
  return $("#" + id).find("dt a span.value").html();
}

$(document).bind('click', function(e) {
  var $clicked = $(e.target);
  if (!$clicked.parents().hasClass("dropdown"))
    $(".dropdown dd ul").hide();
});

$(".dropdown img.flag").toggleClass("flagvisibility");

<div class="selectbox">
  <dl class="dropdown">
    <dt><a href="#" style="padding-top:4px;"><span>신상품순</span></a></dt>
    <dd>
      <ul class="dropdown2">
        <li><a href="#">신상품순</a></li>
        <li><a href="#">인기상품순</a></li>
        <li><a href="#">낮은가격순</a></li>
        <li><a href="#">높은가격순</a></li>
      </ul>
    </dd>
  </dl>
</div>

.desc {
  color: #e8e8e8;
}

.desc a {
  color: #515151;
}

.dropdown {
  width: 103px;
  margin: 0px;
}

.dropdown dd,
.dropdown dt,
.dropdown ul {
  margin: 0px;
  padding: 0px;
}

.dropdown dd {
  position: relative;
}

.dropdown a,
.dropdown a:visited {
  color: #3b3b3b;
  text-decoration: none;
  outline: none;
}

.dropdown a:hover {
  color: #3b3b3b;
}

.dropdown dt a:hover {
  color: #3b3b3b;
  border: 1px solid #9e9e9e;
}

.dropdown dt a {
  background: #fff url('http://imivory.me/img/noname/arrow.png') no-repeat scroll right center;
  display: block;
  padding-right: 20px;
  border: 1px solid #9e9e9e;
  width: 82px;
  height: 33px;
}

.dropdown dt a span {
  cursor: pointer;
  display: block;
  line-height: 29px;
  padding-left: 10px;
}

.dropdown dd ul {
  background: #fff none repeat scroll 0 0;
  border: 1px solid #9e9e9e;
  color: #515151;
  display: none;
  left: 0px;
  padding: 5px 0px;
  position: absolute;
  top: -1px;
  width: auto;
  min-width: 102px;
  list-style: none;
  text-align: left;
}

.dropdown span.value {
  display: none;
}

.dropdown dd ul li a {
  padding: 5px;
  display: block;
  padding-left: 11px;
}

.dropdown dd ul li a:hover {
  background-color: #e8e8e8;
}

.dropdown img.flag {
  border: none;
  vertical-align: middle;
  padding: 11px;
}

.flagvisibility {
  display: none;
}