  We study the error induced by the time discretization of a decoupled
forward-backward stochastic differential equations $(X,Y,Z)$. The forward
component $X$ is the solution of a Brownian stochastic differential equation
and is approximated by a Euler scheme $X^N$ with $N$ time steps. The backward
component is approximated by a backward scheme. Firstly, we prove that the
errors $(Y^N-Y,Z^N-Z)$ measured in the strong $L\_p$-sense ($p \geq 1$) are of
order $N^{-1/2}$ (this generalizes the results by Zhang 2004). Secondly, an
error expansion is derived: surprisingly, the first term is proportional to
$X^N-X$ while residual terms are of order $N^{-1}$.
