We suggest a discretization of the Dirac equation based on time symmetry. This iterative scheme is correct to second order in ε, the lattice distance in time, and can therefore be considered as an improvement to the master equation suggested implicitly by Gaveau et al. (Phys. Rev. Lett. 53 (1984) 419), which generates the Feynman checkerboard propagator. Due to time symmetry this new scheme automatically conserves probability density.