Linear Discriminant Analysis (LDA) has been established as an important means for dimension reduction and decorrelation in speech recognition. The major points of criticism of LDA are that it uses an ad hoc and non-discriminative training criterion, and that the estimation is performed in a separate preprocessing step. This paper presents a new discriminative training method for the estimation of (projecting) linear feature transforms. More precisely, the problem is formulated in the loglinear framework, resulting in a convex optimization problem. Experimental results are provided for a digit string recognition task to compare the performance and robustness of the proposed approach (in combination with ML or MMI optimized acoustic models) with conventional LDA. Also, first experiments for a large vocabulary task are presented.