  We apply a new entropic scheme to study the critical behavior of the
square-lattice Ising model with nearest- and next-nearest-neighbor
antiferromagnetic interactions. Estimates of the present scheme are compared
with those of the Metropolis algorithm. We consider interactions in the range
where superantiferromagnetic (SAF) order appears at low temperatures. A recent
prediction of a first-order transition along a certain range (0.5-1.2) of the
interaction ratio $(R=J_{nnn}/J_{nn})$ is examined by generating accurate data
for large lattices at a particular value of the ratio $(R=1)$. Our study does
not support a first-order transition and a convincing finite-size scaling
analysis of the model is presented, yielding accurate estimates for all
critical exponents for R=1 . The magnetic exponents are found to obey ``weak
universality'' in accordance with a previous conjecture.
