Can the U.S. President undo the executive directive of a former president with his own executive directive?
Yes. Also executive orders can be undo by the Courts. To date, U.S. courts have overturned only two executive orders: the aforementioned Truman order, and a 1996 order issued by President Clinton that attempted to prevent the U.S. government from contracting with organizations that had strike-breakers on the payroll. Congress may overturn an executive order by passing legislation in conflict with it or by refusing to approve funding to enforce it. In the former, the president retains the power to veto such a decision; however, the Congress may override a veto with a two-thirds majority to end an executive order. It has been argued that a Congressional override of an executive order is a nearly impossible event due to the supermajority vote required and the fact that such a vote leaves individual lawmakers very vulnerable to political criticism.