If you have a unipolar stepper motor, you could just use a ULN2x03, ULN2x04 Darlington driver (the "x" is 0 or 8 for 7-channel or 8-channel) for up to 350mA/channel, or ULN2068 Darlington IC for up to 1.2a/channel.
If you use a unipolar stepper as a bipolar stepper, you'll need to use twice the stepper's rated voltage. The added inductance will slow the stepper's response time and maximum speed.
If you omit the L297, you will eliminate the advantage of the chopper drive circuit, which will decrease torque and top speed.
A one-half-H bridge has only one output.
A full-H bridge has two outputs.
A dual H-bridge has four outputs.