Optimization of multiprocessor systems relies heavily on the efficient design of on-chip routing algorithms. Adaptive routing appears to have an extremely significant role in the performance of the Networks-on-Chip. In this paper, a deadlock-free and highly adaptive minimal routing method (HOE) is proposed. Although the Hamiltonian Adaptive Multicast Unicast Model (HAMUM) is able to support a high degree of adaptiveness, it cannot exploit some of the potential alternative paths in routing. By prohibiting the minimum number of turns, our proposed method strives to find the maximum number of alternative paths between each pair of source and destination nodes, without using virtual channels. HOE has also been applied to the Column-Path (CP) routing algorithm to improve its characteristics. The simulation results validate the flexibility of our approach in choosing the appropriate routing path depending on the congestion condition of the network. The better performance of the proposed method is due to its higher degree of adaptiveness which results in less vulnerability to nonuniform factors and a better traffic distribution all over the network.