Higher-band self-trapping and oscillation (rotation) of nonlinear quadruple beams in two-dimensional (2D) square photonic lattices are numerically demonstrated. Under appropriate conditions of nonlinearity, a quadruple-like beam can self-trap into localized modes that reside in the second Bragg reflection gap through single-site excitation. By changing the initial orientation of the incident quadruple beam related to the lattices, periodic oscillations of the localized quadruple mode may be obtained. The localized quadruple state becomes a rotating doubly charged optical vortex (DCV) during rotation and should undergo charge-flipping when the rotating direction is reversed.