You don't have to be religious to have morality.
I'm an agnostic and to me, morality is a code of personal honor. IMO, to have morality one must have a sense of dignity and pride in one self and where we come from. To see yourself not as a lone individual, but as a link in a chain.
My parents came before me, and my children will come after me. I am a part of a greater whole. It is up to me to be the strongest link that I can be, and self control and dignity allows me to do that. The chain may have broken before me and it may break after me, but I'll be damned if it breaks because of me. This is the way I try to live my life.