We propose a new algorithm called Generalized Discriminative Feature Transformation (GDFT) for acoustic models in speech recognition. GDFT is based on Lagrange relaxation on a transformed optimization problem. We show that the existing discriminative feature transformation methods like feature space MMI/MPE (fMMI/MPE), region dependent linear transformation (RDLT), and a non-discriminative feature transformation, constrained maximum likelihood linear regression (CMLLR) are special cases of GDFT. We evaluate the performance of GDFT for Iraqi large vocabulary continuous speech recognition.