1d mark 4 has dual DIGIC IV image processors. there are two processors in the body and they work in turn when taking continuous shots. is it possible that the two processors(sensors) need a calibration?
maybe you can make an experiment, taking 6 continuous shots. supposedly, photo #1, #3, #5 are processed by DIGIC IV sensor #1, and photo #2, #4, #6 are processed by DIGIC IV sensor #2.
If photo #1, #3, #5 are brighter(or darker) than photo #2, #4, #6, maybe the problem is on the sensors.