First consider selling your car private sale to try and get more for it than its wholesale value. Also use your down payment or any other cash available to you to make up as much of the difference as you can. If you still find yourself upside-down, you may consider keeping your current car a little longer and continue paying it off. If all else fails, you can roll the negative equity into the new car. You are in essence financing your negative balance along with the cost of the new car.
Many people continually roll more and more negative equity into new purchases.
Eventually this catches up with them because banks limit the amount that they will lend on each car. I have seen people owe over five thousand dollars more on their car than it is worth. Obviously this is trouble. One option that may help here is leasing. I will explain leasing in detail in the buy vs lease section.