Of course! If the claim is made that you need religion to be moral, then all you need is a counterexample to prove it wrong. I don't have religion, yet I am a moral person (though, moral is subjective), so religion must not be a prerequisite for being moral. Would you commit immoral acts just because you lacked religion? Of course not, it's silly. As a corollary, is adherence to a religion the only thing stopping you from committing those acts? Think about it.
In many cases, the nonreligious and the religious come to the same moral conclusion given a particular scenario, which means that there is some other cause for morality. Morality can be seen in the animal kingdom, and so it would make sense that morality is something that occurs naturally and is not the product of a religion.