While the car is stopped to pick up or drop off a customer, press the brake pedal. Pull gearshift back to "Reverse". As soon as the animated sequence has completed (and you can control the car), put the gearshift back into "Drive" while pressing the accelerator.
Before you press the Start Button hold the Gear Selector in Reverse while holding the Brake and the Accellerator. When you start the level your taxi will be facing the opposite direction. This will force you to take an entirely different route.