  We study the discrete-time approximation for solutions of forward-backward
stochas- tic dierential equations (FBSDEs) with a jump. In this part, we study
the case of Lipschitz generators, and we refer to the second part of this work
[15] for the quadratic case. Our method is based on a result given in the
companion paper [14] which allows to link a FBSDE with a jump with a recursive
system of Brownian FBSDEs. Then we use the classical results on discretization
of Brownian FBSDEs to approximate the recursive system of FBSDEs and we
recombine these approximations to get a dis- cretization of the FBSDE with a
jump. This approach allows to get a convergence rate similar to that of schemes
for Brownian FBSDEs.
