If your challenge is to develop a way of moral thinking that does not include religion in any way; then it is certainly a trivial one. Take consequentialism and Kant's categorical imperative, for example. The two moral theories follow philosophical premises that do not rely at all on religious authority or influence. To simplify, Consequentialism (Utilitarianism) relies on the premise that an action is considered morally right if it causes a greater amount of happiness than sadness in the world; while holding that each human life is equally valuable. The Categorical Imperative states that an action is considered morally right if it is a duty( you do it not because of selfish incentives, but because it is right), or if you choose to follow moral rule A and everyone else did the same, the world would be better. This is an oversimplification, but you get the point.
I hope that answers your question if I understood you correctly.
Utilitarianism, ca