We established a fast Swendsen-Wang algorithm for the two-dimensional Ising model on parallel computers with a high efficiency. On an Intel paragon with 140 processors we reached spin update times of only 14 ns with an efficiency of 89%. This algorithm was used to examine the non-equilibrium relaxation of magnetization and energy in large Ising systems of a size up to 17920 × 17920 spins. Nevertheless we observed still a strong finite-size effect for the magnetization. We assume both magnetization and energy decay to behave like (t + Δ)-λe-bt in an infinitely large system. Thus, for long times magnetization and energy show an exponential, asymtotic time-dependence, implying a critical dynamic exponent z of zero.