As our robotics community advances its understanding toward the optimal design of robotic exoskeletons for human gait training, the question we ask in this paper is how the anterior lunge degree of freedom in the robotic exoskeleton affects human gait training. Answering this question requires both novel robotic design and novel protocols for human gait training to characterize this effect. To the best of the authors' knowledge, this is the first study to characterize the effect of an exoskeleton's degrees of freedom on human gait adaptation. We explored this question using the Active Leg EXoskeleton (ALEX) II. The study presented was performed using ALEX II under the following two configurations: 1) locking the anterior/posterior translation in the exoskeleton, while allowing other degrees-of-freedom (labeled as locked mode) and 2) keeping the anterior/posterior degree of freedom unlocked (labeled as unlocked mode). Healthy subjects walked at self-selected speeds on a treadmill and were trained to walk with a new gait template, scaled down from their normal template. While both groups showed adaptation and retention over a 26-min period following training, the unlocked group showed better performance in terms of adaptation and retention compared with the locked group.