Bipolar stepper motors require both a low-side driver and a high-side driver (see Figure 4). This allows the coils to be biased in both directions, requiring two Half-H drivers (one Full-H bridge). The L293D is an example of a device that can drive these types of stepper motors, see Section 3.1 for additional information.
Bipolar stepper motors only come in a 4-wire configuration and do not have center tap connections. See Figure 5 for the wiring of the bipolar stepper motor.