A two-stage analytical-numerical method is described, which enables to accurately solve the energy eigenvalue problem of a rotating oscillator. First, using a simple analytic algorithm, one constructs reliable Morse approximants to all rotational-vibrational states of the given effective potential. Thereafter, the Schrodinger equation is transformed into an equivalent pair of coupled first-order differential equations (Gordon equations), which are solved numerically. Integration step h = 0.05 angstrom is sufficient to ensure at least 6-digit accuracy for all energy levels of the examined model potential for H-2 molecule. (C) 2008 Elsevier B.V. All rights reserved.