  In this paper we consider the random walk approximation of the solution of a
Markovian BSDE whose terminal condition is a locally H{\"o}lder continuous
function of the Brownian motion. We state the rate of the L 2-convergence of
the approximated solution to the true one. The proof relies in part on growth
and smoothness properties of the solution u of the associated PDE. Here we
improve existing results by showing some properties of the second derivative of
u in space.
