Recent adversarial defense approaches have failed. Untargeted gradient-based attacks cause classifiers to choose any wrong class. Our novel white-box defense tricks untargeted attacks into becoming attacks targeted at designated target classes. From these target classes, we can derive the real classes. Our Target Training defense tricks the minimization at the core of untargeted, gradient-based adversarial attacks: minimize the sum of (1) perturbation and (2) classifier adversarial loss. Target Training changes the classifier minimally, and trains it with additional duplicated points (at 0 distance) labeled with designated classes. These differently-labeled duplicated samples minimize both terms (1) and (2) of the minimization, steering attack convergence to samples of designated classes, from which correct classification is derived. Importantly, Target Training eliminates the need to know the attack and the overhead of generating adversarial samples of attacks that minimize perturbations. We obtain an 86.2% accuracy for CW-L2 (confidence=0) in CIFAR10, exceeding even unsecured classifier accuracy on non-adversarial samples. Target Training presents a fundamental change in adversarial defense strategy.