To elucidate the underlying nature of the hidden order (HO) state in heavy-fermion compound URu(2)Si(2), we measure electrical transport properties of ultraclean crystals in a high field, low temperature regime. Unlike previous studies, the present system with much less impurity scattering resolves a distinct anomaly of the Hall resistivity at H;{*} = 22.5 T, well below the destruction field of the HO phase = or approximately 36 T. In addition, a novel quantum oscillation appears above a magnetic field slightly below H;{*}. These results indicate an abrupt reconstruction of the Fermi surface, which implies a possible phase transition well within the HO phase caused by a band-dependent destruction of the HO parameter.