The methanolysis of beef tallow using potassium hydroxide at several reaction conditions has been studied. The full factorial design applied allowed the evaluation of the most important factors for biodiesel purity and yield, which are, in decreasing order, alcohol:tallow molar ratio (M), alcohol:catalyst mass ratio (C) and reaction time (t). It has also shown that an increase in temperature has a negative influence on purity, while for yield, only the alcohol:tallow molar ratio (M) has a significant positive influence. Quadratic models for purity and yield were obtained through the Doehlert matrix, and the contour line plots of their responses have been superimposed for a simultaneous evaluation of the operating conditions used. The model has also shown to have a good predictive performance for both purity and yield. The final biodiesel product obtained showed to have good quality characteristics, except for its density.