  We propose a new method for generating random correlation matrices that makes
it simple to control both location and dispersion. The method is based on a
vector parameterization, gamma = g(C), which maps any distribution on R^d, d =
n(n-1)/2 to a distribution on the space of non-singular nxn correlation
matrices. Correlation matrices with certain properties, such as being
well-conditioned, having block structures, and having strictly positive
elements, are simple to generate. We compare the new method with existing
methods.
