If all morals were relative, then moral argument would be a complete waste of time. Therefore, there must be objective elements to morality.
Like others here, I do not believe that objective morals exist. But people can still engage in rational moral argument if they agree on common moral axioms. It's much like math in that respect. You can't really prove that the axioms themselves are true, you just have to get people to go along with you on them for the sake of discussion. We might bother agree that we should do whatever provides the greatest good for the greatest many, and then proceed to rationally argue about which course of action/law/whatever would meet that criteria. Or we could agree that we should do whatever the Bible tells us, and proceed to argue over what course of action best conforms to Biblical teachings. Or we could agree that we should do unto others as we would have them do unto us. Or that we should do as we like to others before they do unto us.
I am not aware of any universally-held moral principles. And even if you could name one, that wouldn't prove anything about the objective correctness of that principle; at best, it would prove that societies which adhere to that particular principle are more stable or successful than societies that don't.
Perhaps there are no universally-held moral principles. I would argue that perhaps we should look to evolution for a path- specifically, that efficiency tends to dominate for a reason- it gets things done better. Now I agree that efficiency is somewhat complex- we certainly don't want Hitler's efficiency in eliminating people. -However-, it could be argued that there were very many inneficient things about Hitler's regime and it's those things that truly brought it down. I'm not sure if you're familiar with the works of noted biologist Richard Dawkins? He definitely doesn't like the idea of god, -but-, in the second edition of his book "The Selfish Gene", his last chapter is titled "Good Guys Finish First". In the chapter, I found that he provided conclusive proof that in many social environments, being kind to others was actually an evolutionarily sound principle. He also mentions, however, that one must be wary of others who take but don't give back. I believe that this is the true root of such things as being nicer (and more generous) to those who are nice and generous to you. I even believe that it is the root of revenge/punishment (they are sometimes different, but not always) and I believe is the basis for any sound society.