  Screw instability of the magnetic field connecting a rotating black hole (BH)
with its surrounding disk is discussed based on the model of the coexistence of
the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process
(CEBZMC). A criterion for the screw instability with the state of CEBZMC is
derived based on the calculations of the poloidal and toroidal components of
the magnetic field on the disk. It is shown by the criterion that the screw
instability will occur, if the BH spin and the power-law index for the
variation of the magnetic field on the disk are greater than some critical
values. It turns out that the instability occurs outside some critical radii on
the disk. It is argued that the state of CEBZMC always accompanies the screw
instability. In addtition, we show that the screw instability contributes only
a small fraction of magnetic extraction of energy from a rotating BH.
