A new type of instability of the spiral waves (of numerical simulation) in excitable medium is reported in this paper. In a much smaller region near the spiral tip, we put a weak periodic perturbation which doesn't break the spiral tip. The effect of perturbation is magnified by the spiral and the wave breaks far away from the spiral tip. This type of instability is induced by resonance effects which make the oscillatory of the spiral peak near spiral tip severe. The final state containing several point-defects that are new spiral tips is not the defect-mediated turbulence, and the waves excited from these new tips is in a very stable state. (C) 2016 Elsevier B.V. All rights reserved.