There are so many ways to drive a stepper motor, Here is another circuit
that use 74LS194 4 bit bi-directional universal shift register as a phase
generator and
UDN2543B to drive the unipolar stepper motor. U1 74LS04
provide the necessary clock pulse for the circuit. S1 is the direction
selection switch and S2 turns ON/OFF the motor.

The Stepper motor circuit below only requires a single power source, The maximum power
supply voltage can not exceed +20V.

For additional
information and resources on stepper motor drivers see the