We study the local convergence of a predictor-corrector algorithm for semid
efinite programming problems based on the Monteiro-Zhang unified direction
whose polynomial convergence was recently established by Monteiro. Under st
rict complementarity and nondegeneracy assumptions superlinear convergence
with Q-order 1.5 is proved if the scaling matrices in the corrector step ha
ve bounded condition number. A version of the predictor-corrector algorithm
enjoys quadratic convergence if the scaling matrices in both predictor and
corrector steps have bounded condition numbers. The latter results apply i
n particular to algorithms using the Alizadeh-Haeberly-Overton (AHO) direct
ion since there the scaling matrix is the identity matrix.