  We introduce a discrete time reflected scheme to solve doubly reflected
Backward Stochastic Differential Equations with jumps (in short DRBSDEs),
driven by a Brownian motion and an independent compensated Poisson process. As
in Dumitrescu-Labart (2014), we approximate the Brownian motion and the Poisson
process by two random walks, but contrary to this paper, we discretize directly
the DRBSDE, without using a penalization step. This gives us a fully
implementable scheme, which only depends on one parameter of approximation: the
number of time steps $n$ (contrary to the scheme proposed in Dumitrescu-Labart
(2014), which also depends on the penalization parameter). We prove the
convergence of the scheme, and give some numerical examples.
