Summary: A method for approximating scattered data using multiquadric approximation on a transformed domain region is given. With the imposition of a one-to-one constraint on the domain transformation, all properties of the approximating space carry over. Such a domain transformation is defined in terms of a biquadratic Bézier representation. The parameters in the transformation, and the location of the base points (or knots) in the multiquadric approximation are simultaneously determined using a nonlinear least squares paradigm. The results of some comparisons with previous approaches are given and discussed.