DCook's answer is heading in the right direction, but it's at it from the wrong end.
Don't ask your daughter if she did something wrong, not because she might lie to you, or she might not lie to you, or whether or not you know the answer. That's all coming from a faulty paradigm: that it's expected for your daughter to tell you the truth when you ask her if she did something wrong.
Asking her if she did something wrong is setting her up for failure, whether or not you know the answer. I know it is a "thing" parents like to do, mine did as well, where we say - as you did - "It's not whether you did it or not, but that you tell the truth about it" - but now you're the liar, aren't you? Because it darned tooting is about whether she did it or not. If it doesn't matter whether she did it or not, why are you asking? Some sort of cruel mind game?
Put it to you this way, you're on trial for stealing a car, and the prosecutor asks you "Did you do it?" What are you doing in that scenario? I highly doubt it's admitting fault, unless the prosecutor can already prove it and is offering you a deal.
What you're donig right now is training her to lie well. Because that's the only winning game theory scenario on her end: lying, and lying effectively. Lying and getting caught = bad. Telling the truth = bad. Only lying and not getting caught wins, so - that's what she's learning to do. And kids are smart. She sees how you've set up the game, and the only option you're giving her to win.
Turn the paradigm around, instead. Why are you asking her if she did [something wrong]? Either it's because you know something wrong was done by someone, and you just don't know whom, or because you weren't paying enough attention to know what was done wrong.
If something was done wrong, but you don't know by whom, then the answer is easy: make sure she knows what the actual consequences are for that particular thing happening, not the punitive ones, but just the thing that happens.
Aww, the TV got knocked over and now it doesn't work anymore. Now you won't be able to watch Dora! I'm very sad about that, aren't you? I don't know how it got knocked over, but whomever ran into it, I hope they're more careful in the future!
Hmm, it looks like all of the candy from the candy jar got eaten. I guess I won't be able to buy any more candy, since someone's eating it when they shouldn't. I don't want anyone to get sick, or get cavities, so we'll just have to go without dessert for a while.
Poor Janey! Come here dear. I'm really sorry you got this bruise on your arm. Jill, come over here and look at your sister! I don't know how she got this bruise, but it sure looks painful. She's crying an awful lot. I think maybe the two of you should stop playing for a while and do some quiet reading instead, since Janey got this bruise while you two were playing together. Things must have gotten a bit rougher than she can handle.
In all three of those, no accusation is made, no opportunity for her to lie: just the facts, and what happens as a result. Something that she won't be happy about, more than likely, and perhaps something that will cause her to act better next time.
All that said, the other elephant in the room is why she's lying: because she's worried about being punished. A system of discipline that does not focus on punishment, but instead focuses on development and understanding whys, encourages a child to accurately describe even things they did wrong: because they know you're not going to punish them, but instead you're going to help them learn more about why they should make a different choice in the future.
That's not for everyone, and it's not something even those practicing this method can do perfectly every time - we're all human - but it's something that works for some, and works very well.
But consider this: you say she does [thing she shouldn't do] when you're not around. Guess what: you're going to be not around an awful lot through the next 13 years, and then after that you're going to be not around mostly at all. If the only reason she's not doing [things she shouldn't do] is out of fear of punishment - guess what, those next thirteen years are not going to be much fun, because she's going to have a lot of chances to do things she shouldn't do.
If instead, the goal is teaching her how to make better choices, the how and the why more than the what, you might get to a more comfortable place - one where she's doing positive things.