  We study the square-lattice three-state Potts model with the ferromagnetic
next-nearest-neighbor coupling at finite temperature. Using the
level-spectroscopy method, we numerically analyze the excitation spectrum of
the transfer matrices and precisely determine the global phase diagram. Then we
find that, contrary to a previous result based on the finite-size scaling, the
massless region continues up to the decoupling point with ${\bf Z}_3\times{\bf
Z}_3$ criticality in the antiferromagnetic region. We also check the universal
relations among excitation levels to provide the reliability of our result.
