Let ( ) ( )) be a graph. Let be a group. For let ( ) denotes the order of in Let ( ) be a function. For each edge assign the label | ( ( )) ( ( )) | Let ( ) denote the number of vertices of having label under Also ( ) ( ) respectively denote the number of edges labeled with and not with .Now is called a group difference cordial labeling if | ( ) ( )| for every and | ( ) ( )| . A graph which admits a group difference cordial labeling is called group difference cordial graph. In this paper we fix the group as the group which is the group of fourth roots of unity, that is cyclic with generators We prove that Open ladder, Slanting ladder and further characterized ( ).