If two of the wires are labeled "Ground", these are probably center taps for each coil. Using an Ohm meter, identify each coil's pair of wires (excluding the ground wires). Make note of the coil resistance of each coil. Once each coils wire pair is identified and measured, one ground is probably associated with one coil, the other ground the other coil. Confirm this by measuring between a ground and either side of the associated coil. If each ground wire is a center tap for each coil the resistance will be half of the coil's resitance. You can tape up the center tap ground wires ( don't use them) and run the stepper as a two pole, bi-polar.
I'd also make sure the both ground wires are not connected to the motor casing.