In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further propose to use the approximate maximum of the augmented Lagrangian to improve the convergence rate of alternating direction augmented Lagrangian (ADAL) frameworks. Numerical results are shown, giving some insights on the benefits of the approach.