Monte Carlo simulations are used to analyse the behavior of the extend
ed Ashkin-Teller model in two dimensions from the ratio of the square
of the second moment of the order parameter to its fourth moment. The
critical surface in three dimensional parameter space is calculated in
regions where the Ising transitions are expected. The continuity of t
he order parameter at the critical surface is verified by a finite siz
e scaling analysis for both ferromagnetic and antiferromagnetic parts
of the phase diagram.