Abstract
A new numerical scheme for numerical relativity, based upon Riemann normal coordinates, will be presented. The method will be applied to the construction of initial data for a static Schwarzschild spacetime. It will be shown that the scheme yields second order accurate estimates (in the lattice spacing) for the curvatures of a given metric. However, when used to construct solutions of the constraint equations the method does not appear to produce the correct solution. It is unclear at this stage what the cause of this error is - an error of logic, a numerical error or {\sl quelle horreur} a programming bug.