We introduce a new large margin approach to discriminative training of intractable discrete graphical models. Our approach builds on a convex quadratic programming relaxation of the MAP inference problem. The model parameters are trained directly within this restricted class of energy functions so as to optimize the predictions on the training data. We address the issue of how to parameterize the resulting model and point out its relation to existing approaches. The primary motivation behind our use of the QP relaxation is its computational efficiency; yet, empirically, its predictive accuracy compares favorably to more expensive approaches. This makes it an appealing choice for many practical tasks.