I was asked today by a grandmother how to get her granddaughter (5 or 6) to stop saying "no" every time she was asked to do something. I asked if it was things like, "Would you like to help set the table?" That was exactly the time of things that triggered it. In fact no matter what the grandmother asked the child said no to. In fact what the grandmother thought she was doing was inviting her granddaughter to help. What she was really doing was phrase every request in a way that it turned it into a "yes" or "no" question. At every turn the child said "No."
The solution: Think in terms of options and not as a chance to help. The table needs setting, which are you going to help with, the spoons or the forks. Start simple and don't make the task too large. If the child balks then make it a choice between a big thing, such as setting the whole table or a small thing, only putting on the spoons. The child will choose the easy task. Count this as a success and move on and wait for a few hours before offering the next task. Too often parents who find some success with this immediately move on to a whole series of choices and children don't want to be manipulated and will figure out what is happening. Making choices about three times a day is enough for a start with long periods in between. Over time the child will see that they get to make choices and that the rest of the interactions are positive. They will start taking more responsibility on their own without the need to be directed.
If given an chance children who feel powerless about their lives will take every opportunity to say "No" so don't take it personal. Think of it as a journey where over time you are going to teach her that having control can be positive rather than resulting in a negative interaction.