Quadratic relations in continuous and discrete Painleve equations

The quadratic relations between the solutions of a Painleve equation and th at of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the qua dratic relations existing for the continuous P-II, P-III, P-V and P-VI have analogues as well as consequences in the discrete case. Moreover, the disc rete Painleve equations have quadratic relations of their own without any r eference to the continuous case.