Recently Anderson and Mattingly [Comm. Math. Sci. 9, 301 (2011)] proposed a method which can solve chemical Langevin equations with weak second order accuracy. We extend their work to the discrete chemical jump processes. With slight modification, the method can also solve discrete chemical kinetic systems with weak second order accuracy in the large volume scaling. Especially, this method achieves higher order accuracy than both the Euler τ-leaping and mid-point τ-leaping methods in the sense that the local truncation error for the covariance is of order τ3V−1 when τ = V−β (0 < β < 1) and the system size V → ∞. We present the convergence analysis, numerical stability analysis, and numerical examples. Overall, in the authors’ opinion, the new method is easy to be implemented and good in performance, which is a good candidate among the highly accurate τ-leaping type schemes for discrete chemical reaction systems.