In developing an omnidirectional wheelchair tilted to climb single high steps, we enhanced standard step climbing by introducing a four-wheel drive (4WD). One pair of front and back wheels is connected by transmission belts to rotate in unison with a drive motor, i.e., synchrodrive transmission. To avoid wheel slippage as the mechanism turns, two omniwheels are installed in front and two regular tires in back, enabling the front wheels to slide freely sideways while the two back wheels continuously contact the ground. A third motor on the 4WD platform rotates the chair at the center of the mobile base around the vertical axis. The 4WD enhances step climbing over that of standard wheelchairs, but back wheels limit the step height climbed, meaning that front wheels climb higher steps than back wheels. We analyzed 4WD statics to clarify differences in front and back wheel step climbing, finding that drive torque caused the difference and that this influence depends on the wheelbase and vehicle weight distribution ratio of the front and back wheel axes. We varied the load distribution ratio among wheels to maximize back wheel step climbing. To do so, we developed chair tilting with a linear drive and an inclination sensor. The linear drive changes the chair's tilt angle for keeping the wheelchair statics and to vary positioning of the center of gravity (COG) to enable back wheels to climb steps more efficiently. To confirm the effectiveness of chair tilting in this scheme, we tested step climbing in experiments in which a prototype wheelchair carrying a user climbed a 90 mm step, but the back wheels failed when chair tilting was disabled.