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 circuits below only required a single power source, The maximum power supply voltage can not exceed +20V.