We present the findings for the quantum conductance staircase of holes that is caused by the edge channels in the ultra-shallow p-type silicon quantum well (Si-QW), 2 nm, confined by the δ-barriers heavily doped with boron on the n-type Si (100) surface. This longitudinal quantum conductance staircase, Gxx, is revealed by the voltage applied to the Hall contacts, Vxy, to a maximum of 4e2/h. In addition to the standard plateau, 2e2/h, the variations of the Vxy voltage appear to exhibit the fractional forms of the quantum conductance staircase with the plateaus and steps that bring into correlation respectively with the odd and even fractional values.