The DES key schedule is linear and yet defeats related-key cryptanalysis and other attacks that exploit weaknesses in key schedules, for example the slide attacks. In this paper we present new interesting key-pairs of the DES that can be used in related-key attacks to produce sliding properties of the full-round DES key schedule. This is a sort of key schedule weakness from a slide attack point of view. Our results demonstrate the first known sliding property of the original DES key schedule for its full 16 rounds. Finally, we consider potential applications of these findings in extending the slide attacks.