A new mechanism for negative differential resistance (NDR) originating from local orbital symmetry matching between an electrode and a molecule in a single molecular electronic device is proposed and demonstrated by a joint experimental and theoretical scanning tunneling microscope study of a cobalt phthalocyanines (CoPc) molecule on a gold substrate. For two different metal tips used, Ni and W, NDR occurs only with Ni tips and shows no dependence on the geometrical shape of the tip. Calculations reveal that such a behavior is a result of local orbital symmetry matching between the Ni tip and Co atom.