  The annihilation of vortex-antivortex pairs is a key event in two-dimensional
Bose-Einstein condensates (BECs). It is known that dissipation or a catalyst
vortex is required for the annihilation of the pairs in one-component BECs. We
numerically confirmed in two-component BECs that the pairs can be annihilated
even without any dissipation or catalyst vortices when the intercomponent
interaction is strong. In addition, the pair is recreated alternately in two
components under certain conditions, which we call the recurrence.
