We theoretically study the instability of vortices in pancake-shaped trapped binary Bose–Einstein condensates. We consider that a quantized vortex is at the center of each condensate and two condensates rotate in the opposite directions. The total circulation is zero in BECs having the overlapped vortices because there is relative rotation, which is the rotation of one component in relation to the rotation of the other, but no total rotation, which is the sum of the rotation in both components. We think that the zero-quantum vortices are unstable because this system is locally countersuperflow, two counterpropagating miscible superflows. In a uniform system, the countersuperflow is unstable when the relative velocity between the two condensates exceeds a critical value. We investigate the dynamics of the zero-quantum vortices by numerically solving the Gross–Pitaevskii equations. To understand the results of the numerical calculations, we apply the countersuperflow instability to our present system.