The finite state Markov-Chain approximation method developed by Tauchen (1986) and Tauchen and Hussey (1991) is widely used in economics, finance and econometrics in solving for functional equations where state variables follow an autoregressive process. For highly persistent processes, the method requires a large number of discrete values for the state variables to produce close approximations which leads to an undesirable reduction in computational speed, especially in a multidimensional case. This paper proposes an alternative method of discretizing vector autoregressions. This method can be treated as an extension of Rouwenhorst's (1995) method which, according to our experiments, outperforms the existing methods in the scalar case for highly persistent processes. The new method works well as an approximation that is much more robust to the number of discrete values for a wide range of the parameter space.