A numerical method for a class of forward-backward stochastic
differential equations (FBSDEs) is proposed and analyzed. The method
is designed around the {\it Four Step Scheme} (Douglas-Ma-Protter,
1996) but with a Hermite-spectral method to approximate the solution
to the decoupling quasilinear PDE on the whole space. A rigorous
synthetic error analysis is carried out for a fully discretized
scheme, namely a first-order scheme in time and a Hermite-spectral
scheme in space, of the FBSDEs. Equally important, a systematical
numerical comparison is made between several schemes for the resulting
decoupled forward SDE, including a stochastic version of the
Adams-Bashforth scheme.  It is shown that the stochastic version of
the Adams-Bashforth scheme coupled with the Hermite-spectral method
leads to a convergence rate of $\frac 32$ (in time) which is better
than those in previously published work for the FBSDEs.