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While studying a two-dimensional excitable medium described by the Fitz--Hugh equation on a digital computer a new type of instabilities was discovered which had no analogy in one-dimensional systems. It has been shown that when the wave encounters upon an obstacle the front breaks, diverge, thus destroying the excitation waves. Initiation of such instabilities is associated with critical curvative phenomenon. The instabilities appear when the front curvature in the region of wave break is greater than the critical one for the given medium. The instabilities found are observed when medium excitability is suppressed. This phenomenon may be related to the processes which occur in the damage regions of the myocardium tissue.
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