  In this paper we propose a feasible numerical scheme for high-dimensional,
fully nonlinear parabolic PDEs, which includes the quasi-linear PDE associated
with a coupled FBSDE as a special case. Our paper is strongly motivated by the
remarkable work Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364]
and stays in the paradigm of monotone schemes initiated by Barles and
Souganidis [Asymptot. Anal. 4 (1991) 271-283]. Our scheme weakens a critical
constraint imposed by Fahim, Touzi and Warin (2011), especially when the
generator of the PDE depends only on the diagonal terms of the Hessian matrix.
Several numerical examples, up to dimension 12, are reported.
