We present a new scheme for approximating solutions of forward-backward stochastic differential equations (FBSDEs). The scheme is particularly suitable for fully coupled FBSDEs. The approximation relies on a piecewise in time approximation by minimizing an error functional that measures how well a process triplet satifies the FBSDE. The error functional is minimized in a finite-dimensional linear space based on iterated integrals. We provide sufficient conditions for the approximations to converge at the rate 1/sqrt(N), where N is the time discretization parameter.