The E(1)Sigma(+) 'Rydberg' state of (MgO)-Mg-24-O-16 has been characterized by two-color resonance-enhanced two-photon ionization (R2PI) spectroscopy in the 36000-40000 cm(-1) region. Several rotationally resolved bands, assigned consistently to (MgO)-Mg-24-O-16(E(1)Sigma(+) <-- X(1)Sigma(+)) vibronic transitions, have been analyzed. The effective B-v' (v' = 0 - 8) constants determined exhibit an unusual variation with v'. Possible causes of this variation are discussed. Estimated spectroscopic constants for the E(1)Sigma(+) state are reported. (C) 2004 Elsevier B.V. All rights reserved.