We study numerically the dynamics of spiral waves in an excitable medium with negative restitution. For our study we use two models of the excitable medium: a cellular automaton and a reaction-diffusion model. There are no significant effects of negative restitution as long as the slope of the restitution curve is less steep than -1. In media with slopes steeper than -1, the dynamics of spiral waves can change significantly: (1) the average restitution time jumps to a value where the slope of the restitution curve is about -1; (2) spiral waves can break up into turbulent patterns. We discuss a possible connection between such instabilities and fibrillation in atrial tissue.