How to generate random values in range (-1, 1) such that the total sum is 0?

If the sum is 1, I could just divide the values by their sum. However, this approach is not applicable when the sum is 0.

Maybe I could compute the opposite of each value I sample, so I would always have a pair of numbers, such that their sum is 0. However this approach reduces the "randomness" I would like to have in my random array.

Are there better approaches?