  We develop a new approach for sketching the quantum chromodynamics
phase-diagram within the Nambu--Jona-Lasinio model for arbitrarily large values
of the coupling constant, temperature and chemical potential based upon the
strategy of Lagrange multipliers that constrains the corresponding gap equation
and its mass gradient. Our approach distinguishes continuous from
discountinuous phase transitions and thus is capable of locating the position
of the Critical End Point from the thermodynamical parameters of the model
alone, without direct reference to the chiral susceptibility or any other
observable. The approach can be straightforwardly extended to those effective
chiral quark models with a momentum independent constituent quark mass.
