The purpose of the paper is to compute the action of the Steenrod-Milnor operations on the generators of P2GL2. More precisely, we explicitly determine the action of St(i,j) on the Dickson invariants Q2,0 and Q2,l. The analogous results for p = 2 have been anounced. The rest of the paper contains two sections. The author recall some needed information on the invariant theory. And compute the action of the Steenrod-Milnor operations on the Dickson invariants.