The decay psi(2S)-->K(0)(S)K(0)(L) is observed using psi(2S) data collected with the Beijing Spectrometer at the Beijing Electron-Positron Collider; the branching fraction is determined to be B(psi(2S)-->K(0)(S)K(0)(L))=(5.24+/-0.47+/-0.48)x10(-5). Compared with J/psi-->K(0)(S)K(0)(L), the psi(2S) branching fraction is enhanced relative to the prediction of the perturbative QCD "12%" rule. The result, together with the branching fractions of psi(2S) decays to other pseudoscalar meson pairs (pi(+)pi(-) and K+K-), is used to investigate the relative phase between the three-gluon and the one-photon annihilation amplitudes of psi(2S) decays.