Despite the success of graph neural network models in node classification, edge prediction (the task of predicting missing or potential links between nodes in a graph) remains a challenging problem for these models. A common approach for edge prediction is to first obtain the embeddings of two nodes, and then a predefined scoring function is used to predict the existence of an edge between the two nodes. In this paper, we introduce a new approach called Edge2Node (E2N) which directly obtains an embedding for each edge, without the need for a scoring function. To do this, we create a new graph H based on the graph G given for the edge prediction task, and then reduce the edge prediction task on G to a node classification task on H. Our E2N method can be easily applied to any edge prediction task with superior performance and lower computational costs. Our E2N method beats the best-known methods on the leaderboards for ogbl-ppa, ogbl-collab, and ogbl-ddi datasets by 25.89%, 24.19%, and 0.34% improvements, respectively.