Javascript - Add class to a class (not ID)

In a HTML file i load a javascript file (in the header) which contains some code. In that code it checks if a cookie exists. If the cookie doesn't exists it should add a class to a div which should be matched with a class.

Example:

The class where it should add the class:

<header class="firstClass">

The javascript:

var classcode = document.getElementsByClassName("firstClass");

if (myCookie == null) {
    add class "secondClass" to "firstClass";
}

I've tried several things but I can't get it to work...

I should mention, the javascript file is loaded before the div where the class should be added.