  We derive a new first-order formulation for Einstein's equations which
involves fewer unknowns than other first-order formulations that have been
proposed. The new formulation is based on the 3+1 decomposition with arbitrary
lapse and shift. In the reduction to first order form only 8 particular
combinations of the 18 first derivatives of the spatial metric are introduced.
In the case of linearization about Minkowski space, the new formulation
consists of symmetric hyperbolic system in 14 unknowns, namely the components
of the extrinsic curvature perturbation and the 8 new variables, from whose
solution the metric perturbation can be computed by integration.
