Calculations of hadron masses are done in quenched approximation using gauge held and fermion actions which are both corrected for discretization errors to O(a(2)) at the classical level and which contain tadpole improvement factors. The fermion action has both nearest-neighbour and next-nearest-neighbour couplings in the kinetic and Wilson terms. Simulations done at lattice spacings of 0.27 and 0.4 fm yield hadron masses which are already quite close to experimental values. The results are compared to Wilson action calculations done at comparable lattice spacings.