McEneaney introduced a curse-of-dimensionality free method for solving HJB equations in which the Hamiltonian is a maximum of linear/quadratic forms. The approximation error was shown to be $O(1/(N\tau))$+$O(\sqrt{\tau})$ where $\tau$ is the time discretization size and $N$ is the number of iterations. Here we use a recently established contraction result for the indefinite Riccati flow in Thompson's metric to show that under different technical assumptions, the error is only of $O(e^{-N\tau})+O(\tau)$.