How Can I Delete A Cookie In Internet Explorer - It Works In Mozilla !

I have the following code which deletes, i.e. sets the cookie in the past, a cookie.

var cookie_name = 'memberCookie'
var cookie_date = new Date(); // Current Date & Time
cookie_date.setDate (cookie_date.getDate() - 5);
var cookie = cookie_name + "=; expires=" + cookie_date.toGMTString() + "; path=/";
parent.menu.document.cookie = cookie;
parent.menu.location.reload(1)
parent.menu.document.cookie - this is just the path to the cookie which resides in a frame called menu.

This code works in Mozilla, as it stores the cookie by name i.e. memberCookie, however in Internet Explorer the cookie file is named ti8@localhost[1] which is just my username and server name from uni. Is this the reason it cannot delete the cookie? Or despite the file being called ti8@localhost[1] the cookie is really named memberCookie?

Can anyone please provide any advice for me. Would I need two seperate statements, one which deletes the cookie in Mozilla and one for IE?