Motivated by recent studies on reversible adhesion mechanisms of geckos and insects, we investigate the effect of pre-tension on the orientation-dependent adhesion strength of an elastic tape adhering on a substrate. Our analysis shows that the pre-tension can significantly increase the peel-off force at small peeling angles while decreasing it at large peeling angles, leading to a strongly reversible adhesion. More interestingly, we find that there exists a critical value of pre-tension beyond which the peel-off force plunges to zero at a force-independent critical peeling angle. We further show that the level of pre-tension required for such force-independent detachment at a critical angle can be induced by simply dragging a spatula pad along a substrate at sufficiently low angles. These results provide a feasible explanation of relevant experimental observations on gecko adhesion and suggest possible strategies to design strongly reversible adhesives via pre-tension.