This paper makes two contributions. The first is to propose a new family of copulas for which the copula arguments are uncorrelated but dependent. Specifically, if w₁ and w₂ are the uniform random variables in the copula, they are uncorrelated, but w₁ is correlated with |w₂ − 1/2|. We show how this family of copulas can be applied to the error structure in an econometric production frontier model. The second contribution is to give some general results on how to extend a two-dimensional copula to three or more dimensions. This extension is necessary in our production frontier model when there are multiple inputs, but our results apply more generally to the extension of arbitrary two-dimensional copulas. We also report the results of some simulations and we give an empirical example.