Spontaneous spiral breakup scenarios are investigated in a reaction-diffusion glycolytic medium exhibiting birhythtnic dynamics, in which, depending on the direction the system is driven toward the birhythmic window, near-core breakup and far-field breakup have been observed. Our analysis suggests that the breakup is because the emergence of a second attractor splits the concentration domain that spans the spiral wave activity into two attraction basins, causing that different parts of the spiral evolve, respectively, toward the two limit cycles and then break up. Affected by the attraction strength of the new limit cycle, intermittent breakup behavior is uncovered during the near-core breakup. (C) 2007 Elsevier B.V. All rights reserved.