An Ising model with ferromagnetic nearest-neighbor interactions J1 (J1 > 0) and random next-nearest-neighbor interactions [+ J2 with probability p and - J2 with probability (1 - p); J2 > 0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n = 1, 2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J1 = J2, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures. © 2009 Elsevier B.V. All rights reserved.