How to Delete attachment from an Item in Sharepoint List

public static void DeleteAttachements(int id)

{
using (SPSite site = new SPSite("http://portal"))
{
using (SPWeb web = site.OpenWeb())
{
SPListItem listItem = web.Lists["mylist"].GetItemById(id);
List<string> fileNames = new List<string>();
foreach (string fileName in listItem.Attachments)
{
fileNames.Add(fileName);
}
foreach(string fileName in fileNames)
{
listItem.Attachments.Delete(fileName);
}
listItem.update();
}
}
}