Web design is a difficult work also when we think about to make it compatible with all devices, browsers or OS.

Here is one of a regularly question about “How to remove the dropdown arrow from Select tag” which we could solve it in different way as well.

Firefox, Chrome, Safari:

With CSS3, you can do it with following CSS code:

select 
{
  -webkit-appearance:none;
  -moz-appearance:none;
  -o-appearance:none;
   appearance:none; 
}

IE 10, IE11

From IE10, Microsoft provides a way to do that as following in CSS3:

select::-ms-expand{
  display:none;
}

IE9:

There won’t come with a simple CSS solution for IE9

IE8/IE7:

It seems that it’s very difficult to achieve it in IE8 or IE7

Alternative Soltuion

You might try to use a jQuery plugin: Chosen: http://harvesthq.github.io/chosen/ that might solve this issue for us.