  An Ising model with ferromagnetic nearest-neighbor interactions $J_{1}$
($J_{1}>0$) and random next-nearest-neighbor interactions [$+J_{2}$ with
probability $p$ and $-J_{2}$ with probability $(1-p)$; $J_{2}>0$] 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 $n=1,2, {\rm and} 4$ spins, using the standard
approximation of neglecting correlations. A phase diagram is obtained in the
plane temperature versus $p$, for the particular case $J_{1}=J_{2}$, showing
both superantiferromagnetic (low $p$) and ferromagnetic (higher values of $p$)
orderings at low temperatures.
