Abstract: The concepts of k-order modified double-graphs and k-order modified matrices are introduced. By using them two new expressions of graph determinant C(Y) and k-order cofactor Y(ij)are deduced. Then the modified double-graph method is presented for finding symbolic k-order cofactors. By applying it a multi-layer expansion of Y(ij) can be found directly and efficiently (having no special sign evaluation poblem), and it produces no cancellation terms. Hence it is superior to the previous methods.