We present the arbitrary angular momentum solutions of the Schrodinger equation for a diatomic molecule with the modified Kratzer potential D-e[(r - r(e))/r](2). The bound state energy eigenvalues and the corresponding eigenfunctions are obtained by the use of the Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bound states are calculated for various values of l with n <= 5 and applied to several diatomic molecules. All of these calculations present an effective and methodological procedure under the NU method to investigate the Kratzer's molecular systems. (c) 2005 Elsevier B.V. All rights reserved.