We show that for the Green-Schwarz superstring on AdS5×S5, the Cartan 1-forms associated with the flat currents given by Bena, Polchinski and Roiban [Phys. Rev. D 69 (2004) 046002] also satisfy equations of motion and the Virasoro constraint. Thus one can generate a series of classical solutions with a spectrum parameter from the existing one, and these solutions have the same infinite set of classically conserved quantities.