  We study a discrete-time approximation for solutions of systems of decoupled
forward-backward doubly stochastic differential equations (FBDSDEs). Assuming
that the coefficients are Lipschitz-continuous, we prove the convergence of the
scheme when the step of time discretization, $|\pi|$ goes to zero. The rate of
convergence is exactly equal to $|\pi|^{1/2}$. The proof is based on a
generalization of a remarkable result on the $^{2}$-regularity of the solution
of the backward equation derived by J. Zhang
