Not to be too relativistic about it, but it depends on how you define “moral relativism”. For example, I claim that killing a person isn’t always bad - self-defense is a viable justification, for example. Is this moral relativism? Could be.
What I usually imagine as “moral relativism”, though, is something more. It’s more far-reaching, and more extreme. It may claim, for example, that the act of forbidding women from showing their faces and holding jobs and such is bad for us, but just hunky-dory for Arab nations, because who are we to judge? Terrorists attacked our nation? Well, one man’s terrorist is another man’s freedom-fighter, right? Who are we to judge? A moral absolutist would be more comfortable in saying that oppressing women so is wrong, and terrorists are evil, period.
So, are morals absolute or relative? If there’s a God, and he handed down an Absolute Moral Code, then the question would be easy to answer. If not, then it becomes trickier. For example, if I walk into a stranger’s house, and kill them in their sleep, just so that I can steal their TV, that seems pretty wrong - pretty immoral. In fact, I can’t conceive of a moral code under which this would be acceptable. So, is that an absolute, then? But if so, then where did this absolute come from? I suppose you could argue that most everyone would see this as an immoral act, and thus the moral code is decided by majority. But this presents obvious problems - what if the majority of people decided that the aforementioned murder was acceptable? Would that make it okay? I find it hard to accept that it would. So in the absence of a God, an absolute moral code seems hard to formulate.
So moral relativism it is, then, right? But there’s another problem. If any one set of morals is just as valid as any other, then what gives us the right to judge anyone? Your moral code may say that kicking you in the shin just for fun is wrong, but mine says it’s all good, so there. How do you argue with that? You’re reduced to morals-by-majority, again.
However, maybe there is an absolute moral code, even if there’s no divine being to hand it down. Maybe the moral code is hard-wired into every man, woman, and child - part of our genetic code. You have 46 genes, every cell has a nucleous, and by the way, murder is bad. Such a moral code could’ve been implemented as a means of perpetuating the species - certainly, a species that doesn’t have a problem with killing each other isn’t going to last long. And so we evolved with the belief that X is wrong, and Y is right, and… well, here we are. But if people are hard-wired with a moral code, then why do people do bad things? Well, why do some people get sick more easily? Why do some people have Down’s Syndrome? Genetic defects. Predisposition to be a prick. Or maybe our moral encoding is something subtle, like our handedness. A righty can learn to be a lefty, defying their genes. And maybe a nice person can learn to be a right bastard.
Or maybe I’m just full of shit. 
Jeff