Graph theory is an incredibly important part and is widely used in the world around us. Graph theory is an area in discrete mathematics, which studies configurations (called graphs) involving a set of vertices interconnected by edges. The Orthogonal Double Covers (ODC) is a branch of graph theory. In this paper, we are interested in finding new symmetric starter vectors using the Cartesian product methods, such as symmetric starter vectors of complete bipartite graphs with complete bipartite graphs, disjoint copies of paths with stars, stars with caterpillars, disjoint copies of stars with caterpillars, disjoint copies of cycles with caterpillars, disjoint copies of paths with caterpillars, and complete bipartite graphs with caterpillars. Then we use these symmetric starter vectors to get the enormous graphs and construct the ODCs.