  Using a real-space renormalization group procedure with no adjustable
parameters, we investigate the Blume-Emery-Griffiths model on the square
lattice. The formalism respects sublattice symmetry, allowing the study of both
signs of K, the biquadratic exchange coupling. Our results for K>0 are compared
with other renormalization group calculations and with exact results, in order
to assess the magnitude of the errors introduced by our approximate
calculation. The quantitative agreement is excellent; values for critical
parameters differ, in some cases, by less than 1% from exact ones. For K<0, our
results lead to a rich phase diagram, with antiquadrupolar and ferromagnetic
ordered phases. Contrarily to Monte Carlo simulations, these two phases meet
only at zero temperature. Both antiquadrupolar-disordered and
ferromagnetic-disordered transitions are found to be continuous and no
ferrimagnetic phase is found.
