The original axisymmetric, stationary electrodynamic model of the central engine in an active galactic nucleus proposed by Macdonald and Thorne consists of a supermassive black hole with magnetic field lines that pass through the region just outside the event horizon of the black hole. Each magnetic field line rotates with a constant angular velocity which will exceed the speed of light at large radii. Even though the field lines are purely mathematical entities this condition sets a stringent physical constraint on the motion of the magnetic field lines and the particles on them. In this paper we will show that we can remove this auxiliary constraint in our model by allowing nonstationary processes. As a result the magnetic field lines can be twisted and wound up in a region lying outside of the quasi-stationary magnetosphere of the black hole. We conclude that astrophysical jets are formed in that region due to the twisted and wound magnetic field lines powered by the Blandford-Znajek process and the other driving forces.